Classical and multilinear harmonic analysis.: Vol. 1 /
"This two-volume text in harmonic analysis introduces a wealth of analytical results and techniques. It is largely self-contained, and will be useful to graduate students and researchers in both pure and applied analysis. Numerous exercises and problems make the text suitable for self-study and...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York :
Cambridge University Press,
2013.
|
| Schriftenreihe: | Cambridge studies in advanced mathematics ;
137. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | "This two-volume text in harmonic analysis introduces a wealth of analytical results and techniques. It is largely self-contained, and will be useful to graduate students and researchers in both pure and applied analysis. Numerous exercises and problems make the text suitable for self-study and the classroom alike. This first volume starts with classical one-dimensional topics: Fourier series; harmonic functions; Hilbert transform. Then the higher-dimensional Calderón-Zygmund and Littlewood-Paley theories are developed. Probabilistic methods and their applications are discussed, as are applications of harmonic analysis to partial differential equations. The volume concludes with an introduction to the Weyl calculus. The second volume goes beyond the classical to the highly contemporary, and focuses on multilinear aspects of harmonic analysis: the bilinear Hilbert transform; Coifman-Meyer theory; Carleson's resolution of the Lusin conjecture; Calderón's commutators and the Cauchy integral on Lipschitz curves. The material in this volume has not previously appeared together in book form"-- |
| Beschreibung: | 1 online resource |
| Bibliographie: | Includes bibliographical references. |
| ISBN: | 9781139624749 1139624741 |
Internformat
MARC
| LEADER | 00000cam a2200000 a 4500 | ||
|---|---|---|---|
| 001 | ZDB-4-EBA-ocn824529294 | ||
| 003 | OCoLC | ||
| 005 | 20241004212047.0 | ||
| 006 | m o d | ||
| 007 | cr cnu---unuuu | ||
| 008 | 130117s2013 nyu ob 000 0 eng d | ||
| 040 | |a N$T |b eng |e pn |c N$T |d OCLCF |d CNCGM |d OCLCQ |d VLY |d AGLDB |d OCLCQ |d OCLCO |d OCLCQ |d OCLCO |d OCLCL | ||
| 019 | |a 1182856888 | ||
| 020 | |a 9781139624749 |q (electronic bk.) | ||
| 020 | |a 1139624741 |q (electronic bk.) | ||
| 035 | |a (OCoLC)824529294 |z (OCoLC)1182856888 | ||
| 050 | 4 | |a QA403 | |
| 072 | 7 | |a MAT |x 016000 |2 bisacsh | |
| 082 | 7 | |a 515/.2422 |2 23 | |
| 084 | |a MAT034000 |2 bisacsh | ||
| 049 | |a MAIN | ||
| 100 | 1 | |a Muscalu, Camil. | |
| 245 | 1 | 0 | |a Classical and multilinear harmonic analysis. |n Vol. 1 / |c Camil Muscalu and Wilhelm Schlag. |
| 260 | |a New York : |b Cambridge University Press, |c 2013. | ||
| 300 | |a 1 online resource | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Cambridge studies in advanced mathematics ; |v 137 | |
| 504 | |a Includes bibliographical references. | ||
| 520 | |a "This two-volume text in harmonic analysis introduces a wealth of analytical results and techniques. It is largely self-contained, and will be useful to graduate students and researchers in both pure and applied analysis. Numerous exercises and problems make the text suitable for self-study and the classroom alike. This first volume starts with classical one-dimensional topics: Fourier series; harmonic functions; Hilbert transform. Then the higher-dimensional Calderón-Zygmund and Littlewood-Paley theories are developed. Probabilistic methods and their applications are discussed, as are applications of harmonic analysis to partial differential equations. The volume concludes with an introduction to the Weyl calculus. The second volume goes beyond the classical to the highly contemporary, and focuses on multilinear aspects of harmonic analysis: the bilinear Hilbert transform; Coifman-Meyer theory; Carleson's resolution of the Lusin conjecture; Calderón's commutators and the Cauchy integral on Lipschitz curves. The material in this volume has not previously appeared together in book form"-- |c Provided by publisher. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Preface; Acknowledgements; 1 Fourier series: convergence and summability; 1.1 The basics: partial sums and the Dirichlet kernel; 1.2 Approximate identities, Fej ́er kernel; 1.3 The Lp convergence of partial sums; 1.4 Regularity and Fourier series; 1.5 Higher dimensions; 1.6 Interpolation of operators; Notes; Problems; Problems; Problems; Problems; Problems; Problems; Problems; Problems; Problems; Problems; Problems; Problems; 2 Harmonic functions; Poisson kernel; 2.1 Harmonic functions; 2.2 The Poisson kernel; 2.3 The Hardy-Littlewood maximal function | |
| 505 | 8 | |a 2.4 Almost everywhere convergence2.5 Weighted estimates for maximal functions; Notes; 3 Conjugate harmonic functions; Hilbert transform; 3.1 Hardy spaces of analytic functions; 3.2 Riesz theorems; 3.3 Definition and simple properties of the conjugate function; 3.4 The weak-L1 bound on the maximal function; 3.5 The Hilbert transform; 3.6 Convergence of Fourier series in Lp; Notes; 4 The Fourier transform on Rd and on LCA groups; 4.1 The Euclidean Fourier transform; 4.2 Method of stationary or nonstationary phases; 4.3 The Fourier transform on locally compact Abelian groups; Notes | |
| 505 | 8 | |a 5 Introduction to probability theory5.1 Probability spaces; independence; 5.2 Sums of independent variables; 5.3 Conditional expectations; martingales; Notes; 6 Fourier series and randomness; 6.1 Fourier series on L1(T): pointwise questions; 6.2 Random Fourier series: the basics; 6.3 Sidon sets; Notes; 7 Calder ́on-Zygmund theory of singular integrals; 7.1 Calder ́on-Zygmund kernels; 7.2 The Laplacian: Riesz transforms and fractional integration; 7.3 Almost everywhere convergence; homogeneous kernels; 7.4 Bounded mean oscillation space; 7.5 Singular integrals and Ap weights | |
| 505 | 8 | |a 7.6 A glimpse of H1-BMO duality and further remarksNotes; 8 Littlewood-Paley theory; 8.1 The Mikhlin multiplier theorem; 8.2 Littlewood-Paley square-function estimate; 8.3 Calderon-Zygmund H ̈older spaces, and Schauder estimates; 8.4 The Haar functions; dyadic harmonic analysis; 8.5 Oscillatory multipliers; Notes; 9 Almost orthogonality; 9.1 Cotlar's lemma; 9.2 Calderon-Vaillancourt theorem; 9.3 Hardy's inequality; 9.4 The T(1) theorem via Haar functions; 9.5 Carleson measures, BMO, and T(1); Notes; 10 The uncertainty principle; 10.1 Bernstein's bound and Heisenberg's uncertainty principle | |
| 505 | 8 | |a 10.2 The Amrein-Berthier theorem10.3 The Logvinenko-Sereda theorem; 10.4 Solvability of constant-coefficient linear PDEs; Notes; 11 Fourier restriction and applications; 11.1 The Tomas-Stein theorem; 11.2 The endpoint; 11.3 Restriction and PDE; Strichartz estimates; 11.4 Optimal two-dimensional restriction; Notes; 12 Introduction to the Weyl calculus; 12.1 Motivation, definitions, basic properties; 12.2 Adjoints and compositions; 12.3 The L2 theory; 12.4 A phase-space transform; Notes; References; Index | |
| 650 | 0 | |a Harmonic analysis. |0 http://id.loc.gov/authorities/subjects/sh85058939 | |
| 650 | 6 | |a Analyse harmonique. | |
| 650 | 7 | |a MATHEMATICS |x Mathematical Analysis. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Infinity. |2 bisacsh | |
| 650 | 7 | |a Harmonic analysis |2 fast | |
| 700 | 1 | |a Schlag, Wilhelm, |d 1969- |0 http://id.loc.gov/authorities/names/no2012089666 | |
| 758 | |i has work: |a Volume 1 Classical and multilinear harmonic analysis (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGFDW3f6xRRbMg6TpdT9ym |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 830 | 0 | |a Cambridge studies in advanced mathematics ; |v 137. |0 http://id.loc.gov/authorities/names/n84708314 | |
| 856 | 4 | 0 | |l FWS01 |p ZDB-4-EBA |q FWS_PDA_EBA |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=508258 |3 Volltext |
| 938 | |a EBSCOhost |b EBSC |n 508258 | ||
| 994 | |a 92 |b GEBAY | ||
| 912 | |a ZDB-4-EBA | ||
| 049 | |a DE-863 | ||
Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn824529294 |
|---|---|
| _version_ | 1816882219817369601 |
| adam_text | |
| any_adam_object | |
| author | Muscalu, Camil |
| author2 | Schlag, Wilhelm, 1969- |
| author2_role | |
| author2_variant | w s ws |
| author_GND | http://id.loc.gov/authorities/names/no2012089666 |
| author_facet | Muscalu, Camil Schlag, Wilhelm, 1969- |
| author_role | |
| author_sort | Muscalu, Camil |
| author_variant | c m cm |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA403 |
| callnumber-raw | QA403 |
| callnumber-search | QA403 |
| callnumber-sort | QA 3403 |
| callnumber-subject | QA - Mathematics |
| collection | ZDB-4-EBA |
| contents | Preface; Acknowledgements; 1 Fourier series: convergence and summability; 1.1 The basics: partial sums and the Dirichlet kernel; 1.2 Approximate identities, Fej ́er kernel; 1.3 The Lp convergence of partial sums; 1.4 Regularity and Fourier series; 1.5 Higher dimensions; 1.6 Interpolation of operators; Notes; Problems; Problems; Problems; Problems; Problems; Problems; Problems; Problems; Problems; Problems; Problems; Problems; 2 Harmonic functions; Poisson kernel; 2.1 Harmonic functions; 2.2 The Poisson kernel; 2.3 The Hardy-Littlewood maximal function 2.4 Almost everywhere convergence2.5 Weighted estimates for maximal functions; Notes; 3 Conjugate harmonic functions; Hilbert transform; 3.1 Hardy spaces of analytic functions; 3.2 Riesz theorems; 3.3 Definition and simple properties of the conjugate function; 3.4 The weak-L1 bound on the maximal function; 3.5 The Hilbert transform; 3.6 Convergence of Fourier series in Lp; Notes; 4 The Fourier transform on Rd and on LCA groups; 4.1 The Euclidean Fourier transform; 4.2 Method of stationary or nonstationary phases; 4.3 The Fourier transform on locally compact Abelian groups; Notes 5 Introduction to probability theory5.1 Probability spaces; independence; 5.2 Sums of independent variables; 5.3 Conditional expectations; martingales; Notes; 6 Fourier series and randomness; 6.1 Fourier series on L1(T): pointwise questions; 6.2 Random Fourier series: the basics; 6.3 Sidon sets; Notes; 7 Calder ́on-Zygmund theory of singular integrals; 7.1 Calder ́on-Zygmund kernels; 7.2 The Laplacian: Riesz transforms and fractional integration; 7.3 Almost everywhere convergence; homogeneous kernels; 7.4 Bounded mean oscillation space; 7.5 Singular integrals and Ap weights 7.6 A glimpse of H1-BMO duality and further remarksNotes; 8 Littlewood-Paley theory; 8.1 The Mikhlin multiplier theorem; 8.2 Littlewood-Paley square-function estimate; 8.3 Calderon-Zygmund H ̈older spaces, and Schauder estimates; 8.4 The Haar functions; dyadic harmonic analysis; 8.5 Oscillatory multipliers; Notes; 9 Almost orthogonality; 9.1 Cotlar's lemma; 9.2 Calderon-Vaillancourt theorem; 9.3 Hardy's inequality; 9.4 The T(1) theorem via Haar functions; 9.5 Carleson measures, BMO, and T(1); Notes; 10 The uncertainty principle; 10.1 Bernstein's bound and Heisenberg's uncertainty principle 10.2 The Amrein-Berthier theorem10.3 The Logvinenko-Sereda theorem; 10.4 Solvability of constant-coefficient linear PDEs; Notes; 11 Fourier restriction and applications; 11.1 The Tomas-Stein theorem; 11.2 The endpoint; 11.3 Restriction and PDE; Strichartz estimates; 11.4 Optimal two-dimensional restriction; Notes; 12 Introduction to the Weyl calculus; 12.1 Motivation, definitions, basic properties; 12.2 Adjoints and compositions; 12.3 The L2 theory; 12.4 A phase-space transform; Notes; References; Index |
| ctrlnum | (OCoLC)824529294 |
| dewey-full | 515/.2422 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.2422 |
| dewey-search | 515/.2422 |
| dewey-sort | 3515 42422 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>06043cam a2200541 a 4500</leader><controlfield tag="001">ZDB-4-EBA-ocn824529294</controlfield><controlfield tag="003">OCoLC</controlfield><controlfield tag="005">20241004212047.0</controlfield><controlfield tag="006">m o d </controlfield><controlfield tag="007">cr cnu---unuuu</controlfield><controlfield tag="008">130117s2013 nyu ob 000 0 eng d</controlfield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">N$T</subfield><subfield code="b">eng</subfield><subfield code="e">pn</subfield><subfield code="c">N$T</subfield><subfield code="d">OCLCF</subfield><subfield code="d">CNCGM</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">VLY</subfield><subfield code="d">AGLDB</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCL</subfield></datafield><datafield tag="019" ind1=" " ind2=" "><subfield code="a">1182856888</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781139624749</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1139624741</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)824529294</subfield><subfield code="z">(OCoLC)1182856888</subfield></datafield><datafield tag="050" ind1=" " ind2="4"><subfield code="a">QA403</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">MAT</subfield><subfield code="x">016000</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="082" ind1="7" ind2=" "><subfield code="a">515/.2422</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT034000</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">MAIN</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Muscalu, Camil.</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Classical and multilinear harmonic analysis.</subfield><subfield code="n">Vol. 1 /</subfield><subfield code="c">Camil Muscalu and Wilhelm Schlag.</subfield></datafield><datafield tag="260" ind1=" " ind2=" "><subfield code="a">New York :</subfield><subfield code="b">Cambridge University Press,</subfield><subfield code="c">2013.</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Cambridge studies in advanced mathematics ;</subfield><subfield code="v">137</subfield></datafield><datafield tag="504" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">"This two-volume text in harmonic analysis introduces a wealth of analytical results and techniques. It is largely self-contained, and will be useful to graduate students and researchers in both pure and applied analysis. Numerous exercises and problems make the text suitable for self-study and the classroom alike. This first volume starts with classical one-dimensional topics: Fourier series; harmonic functions; Hilbert transform. Then the higher-dimensional Calderón-Zygmund and Littlewood-Paley theories are developed. Probabilistic methods and their applications are discussed, as are applications of harmonic analysis to partial differential equations. The volume concludes with an introduction to the Weyl calculus. The second volume goes beyond the classical to the highly contemporary, and focuses on multilinear aspects of harmonic analysis: the bilinear Hilbert transform; Coifman-Meyer theory; Carleson's resolution of the Lusin conjecture; Calderón's commutators and the Cauchy integral on Lipschitz curves. The material in this volume has not previously appeared together in book form"--</subfield><subfield code="c">Provided by publisher.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Print version record.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">Preface; Acknowledgements; 1 Fourier series: convergence and summability; 1.1 The basics: partial sums and the Dirichlet kernel; 1.2 Approximate identities, Fej ́er kernel; 1.3 The Lp convergence of partial sums; 1.4 Regularity and Fourier series; 1.5 Higher dimensions; 1.6 Interpolation of operators; Notes; Problems; Problems; Problems; Problems; Problems; Problems; Problems; Problems; Problems; Problems; Problems; Problems; 2 Harmonic functions; Poisson kernel; 2.1 Harmonic functions; 2.2 The Poisson kernel; 2.3 The Hardy-Littlewood maximal function</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">2.4 Almost everywhere convergence2.5 Weighted estimates for maximal functions; Notes; 3 Conjugate harmonic functions; Hilbert transform; 3.1 Hardy spaces of analytic functions; 3.2 Riesz theorems; 3.3 Definition and simple properties of the conjugate function; 3.4 The weak-L1 bound on the maximal function; 3.5 The Hilbert transform; 3.6 Convergence of Fourier series in Lp; Notes; 4 The Fourier transform on Rd and on LCA groups; 4.1 The Euclidean Fourier transform; 4.2 Method of stationary or nonstationary phases; 4.3 The Fourier transform on locally compact Abelian groups; Notes</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">5 Introduction to probability theory5.1 Probability spaces; independence; 5.2 Sums of independent variables; 5.3 Conditional expectations; martingales; Notes; 6 Fourier series and randomness; 6.1 Fourier series on L1(T): pointwise questions; 6.2 Random Fourier series: the basics; 6.3 Sidon sets; Notes; 7 Calder ́on-Zygmund theory of singular integrals; 7.1 Calder ́on-Zygmund kernels; 7.2 The Laplacian: Riesz transforms and fractional integration; 7.3 Almost everywhere convergence; homogeneous kernels; 7.4 Bounded mean oscillation space; 7.5 Singular integrals and Ap weights</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">7.6 A glimpse of H1-BMO duality and further remarksNotes; 8 Littlewood-Paley theory; 8.1 The Mikhlin multiplier theorem; 8.2 Littlewood-Paley square-function estimate; 8.3 Calderon-Zygmund H ̈older spaces, and Schauder estimates; 8.4 The Haar functions; dyadic harmonic analysis; 8.5 Oscillatory multipliers; Notes; 9 Almost orthogonality; 9.1 Cotlar's lemma; 9.2 Calderon-Vaillancourt theorem; 9.3 Hardy's inequality; 9.4 The T(1) theorem via Haar functions; 9.5 Carleson measures, BMO, and T(1); Notes; 10 The uncertainty principle; 10.1 Bernstein's bound and Heisenberg's uncertainty principle</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">10.2 The Amrein-Berthier theorem10.3 The Logvinenko-Sereda theorem; 10.4 Solvability of constant-coefficient linear PDEs; Notes; 11 Fourier restriction and applications; 11.1 The Tomas-Stein theorem; 11.2 The endpoint; 11.3 Restriction and PDE; Strichartz estimates; 11.4 Optimal two-dimensional restriction; Notes; 12 Introduction to the Weyl calculus; 12.1 Motivation, definitions, basic properties; 12.2 Adjoints and compositions; 12.3 The L2 theory; 12.4 A phase-space transform; Notes; References; Index</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Harmonic analysis.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85058939</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Analyse harmonique.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS</subfield><subfield code="x">Mathematical Analysis.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS</subfield><subfield code="x">Infinity.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Harmonic analysis</subfield><subfield code="2">fast</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Schlag, Wilhelm,</subfield><subfield code="d">1969-</subfield><subfield code="0">http://id.loc.gov/authorities/names/no2012089666</subfield></datafield><datafield tag="758" ind1=" " ind2=" "><subfield code="i">has work:</subfield><subfield code="a">Volume 1 Classical and multilinear harmonic analysis (Text)</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PCGFDW3f6xRRbMg6TpdT9ym</subfield><subfield code="4">https://id.oclc.org/worldcat/ontology/hasWork</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Cambridge studies in advanced mathematics ;</subfield><subfield code="v">137.</subfield><subfield code="0">http://id.loc.gov/authorities/names/n84708314</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="l">FWS01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=508258</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBSCOhost</subfield><subfield code="b">EBSC</subfield><subfield code="n">508258</subfield></datafield><datafield tag="994" ind1=" " ind2=" "><subfield code="a">92</subfield><subfield code="b">GEBAY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-863</subfield></datafield></record></collection> |
| id | ZDB-4-EBA-ocn824529294 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:25:08Z |
| institution | BVB |
| isbn | 9781139624749 1139624741 |
| language | English |
| oclc_num | 824529294 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource |
| psigel | ZDB-4-EBA |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Cambridge University Press, |
| record_format | marc |
| series | Cambridge studies in advanced mathematics ; |
| series2 | Cambridge studies in advanced mathematics ; |
| spelling | Muscalu, Camil. Classical and multilinear harmonic analysis. Vol. 1 / Camil Muscalu and Wilhelm Schlag. New York : Cambridge University Press, 2013. 1 online resource text txt rdacontent computer c rdamedia online resource cr rdacarrier Cambridge studies in advanced mathematics ; 137 Includes bibliographical references. "This two-volume text in harmonic analysis introduces a wealth of analytical results and techniques. It is largely self-contained, and will be useful to graduate students and researchers in both pure and applied analysis. Numerous exercises and problems make the text suitable for self-study and the classroom alike. This first volume starts with classical one-dimensional topics: Fourier series; harmonic functions; Hilbert transform. Then the higher-dimensional Calderón-Zygmund and Littlewood-Paley theories are developed. Probabilistic methods and their applications are discussed, as are applications of harmonic analysis to partial differential equations. The volume concludes with an introduction to the Weyl calculus. The second volume goes beyond the classical to the highly contemporary, and focuses on multilinear aspects of harmonic analysis: the bilinear Hilbert transform; Coifman-Meyer theory; Carleson's resolution of the Lusin conjecture; Calderón's commutators and the Cauchy integral on Lipschitz curves. The material in this volume has not previously appeared together in book form"-- Provided by publisher. Print version record. Preface; Acknowledgements; 1 Fourier series: convergence and summability; 1.1 The basics: partial sums and the Dirichlet kernel; 1.2 Approximate identities, Fej ́er kernel; 1.3 The Lp convergence of partial sums; 1.4 Regularity and Fourier series; 1.5 Higher dimensions; 1.6 Interpolation of operators; Notes; Problems; Problems; Problems; Problems; Problems; Problems; Problems; Problems; Problems; Problems; Problems; Problems; 2 Harmonic functions; Poisson kernel; 2.1 Harmonic functions; 2.2 The Poisson kernel; 2.3 The Hardy-Littlewood maximal function 2.4 Almost everywhere convergence2.5 Weighted estimates for maximal functions; Notes; 3 Conjugate harmonic functions; Hilbert transform; 3.1 Hardy spaces of analytic functions; 3.2 Riesz theorems; 3.3 Definition and simple properties of the conjugate function; 3.4 The weak-L1 bound on the maximal function; 3.5 The Hilbert transform; 3.6 Convergence of Fourier series in Lp; Notes; 4 The Fourier transform on Rd and on LCA groups; 4.1 The Euclidean Fourier transform; 4.2 Method of stationary or nonstationary phases; 4.3 The Fourier transform on locally compact Abelian groups; Notes 5 Introduction to probability theory5.1 Probability spaces; independence; 5.2 Sums of independent variables; 5.3 Conditional expectations; martingales; Notes; 6 Fourier series and randomness; 6.1 Fourier series on L1(T): pointwise questions; 6.2 Random Fourier series: the basics; 6.3 Sidon sets; Notes; 7 Calder ́on-Zygmund theory of singular integrals; 7.1 Calder ́on-Zygmund kernels; 7.2 The Laplacian: Riesz transforms and fractional integration; 7.3 Almost everywhere convergence; homogeneous kernels; 7.4 Bounded mean oscillation space; 7.5 Singular integrals and Ap weights 7.6 A glimpse of H1-BMO duality and further remarksNotes; 8 Littlewood-Paley theory; 8.1 The Mikhlin multiplier theorem; 8.2 Littlewood-Paley square-function estimate; 8.3 Calderon-Zygmund H ̈older spaces, and Schauder estimates; 8.4 The Haar functions; dyadic harmonic analysis; 8.5 Oscillatory multipliers; Notes; 9 Almost orthogonality; 9.1 Cotlar's lemma; 9.2 Calderon-Vaillancourt theorem; 9.3 Hardy's inequality; 9.4 The T(1) theorem via Haar functions; 9.5 Carleson measures, BMO, and T(1); Notes; 10 The uncertainty principle; 10.1 Bernstein's bound and Heisenberg's uncertainty principle 10.2 The Amrein-Berthier theorem10.3 The Logvinenko-Sereda theorem; 10.4 Solvability of constant-coefficient linear PDEs; Notes; 11 Fourier restriction and applications; 11.1 The Tomas-Stein theorem; 11.2 The endpoint; 11.3 Restriction and PDE; Strichartz estimates; 11.4 Optimal two-dimensional restriction; Notes; 12 Introduction to the Weyl calculus; 12.1 Motivation, definitions, basic properties; 12.2 Adjoints and compositions; 12.3 The L2 theory; 12.4 A phase-space transform; Notes; References; Index Harmonic analysis. http://id.loc.gov/authorities/subjects/sh85058939 Analyse harmonique. MATHEMATICS Mathematical Analysis. bisacsh MATHEMATICS Infinity. bisacsh Harmonic analysis fast Schlag, Wilhelm, 1969- http://id.loc.gov/authorities/names/no2012089666 has work: Volume 1 Classical and multilinear harmonic analysis (Text) https://id.oclc.org/worldcat/entity/E39PCGFDW3f6xRRbMg6TpdT9ym https://id.oclc.org/worldcat/ontology/hasWork Cambridge studies in advanced mathematics ; 137. http://id.loc.gov/authorities/names/n84708314 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=508258 Volltext |
| spellingShingle | Muscalu, Camil Classical and multilinear harmonic analysis. Cambridge studies in advanced mathematics ; Preface; Acknowledgements; 1 Fourier series: convergence and summability; 1.1 The basics: partial sums and the Dirichlet kernel; 1.2 Approximate identities, Fej ́er kernel; 1.3 The Lp convergence of partial sums; 1.4 Regularity and Fourier series; 1.5 Higher dimensions; 1.6 Interpolation of operators; Notes; Problems; Problems; Problems; Problems; Problems; Problems; Problems; Problems; Problems; Problems; Problems; Problems; 2 Harmonic functions; Poisson kernel; 2.1 Harmonic functions; 2.2 The Poisson kernel; 2.3 The Hardy-Littlewood maximal function 2.4 Almost everywhere convergence2.5 Weighted estimates for maximal functions; Notes; 3 Conjugate harmonic functions; Hilbert transform; 3.1 Hardy spaces of analytic functions; 3.2 Riesz theorems; 3.3 Definition and simple properties of the conjugate function; 3.4 The weak-L1 bound on the maximal function; 3.5 The Hilbert transform; 3.6 Convergence of Fourier series in Lp; Notes; 4 The Fourier transform on Rd and on LCA groups; 4.1 The Euclidean Fourier transform; 4.2 Method of stationary or nonstationary phases; 4.3 The Fourier transform on locally compact Abelian groups; Notes 5 Introduction to probability theory5.1 Probability spaces; independence; 5.2 Sums of independent variables; 5.3 Conditional expectations; martingales; Notes; 6 Fourier series and randomness; 6.1 Fourier series on L1(T): pointwise questions; 6.2 Random Fourier series: the basics; 6.3 Sidon sets; Notes; 7 Calder ́on-Zygmund theory of singular integrals; 7.1 Calder ́on-Zygmund kernels; 7.2 The Laplacian: Riesz transforms and fractional integration; 7.3 Almost everywhere convergence; homogeneous kernels; 7.4 Bounded mean oscillation space; 7.5 Singular integrals and Ap weights 7.6 A glimpse of H1-BMO duality and further remarksNotes; 8 Littlewood-Paley theory; 8.1 The Mikhlin multiplier theorem; 8.2 Littlewood-Paley square-function estimate; 8.3 Calderon-Zygmund H ̈older spaces, and Schauder estimates; 8.4 The Haar functions; dyadic harmonic analysis; 8.5 Oscillatory multipliers; Notes; 9 Almost orthogonality; 9.1 Cotlar's lemma; 9.2 Calderon-Vaillancourt theorem; 9.3 Hardy's inequality; 9.4 The T(1) theorem via Haar functions; 9.5 Carleson measures, BMO, and T(1); Notes; 10 The uncertainty principle; 10.1 Bernstein's bound and Heisenberg's uncertainty principle 10.2 The Amrein-Berthier theorem10.3 The Logvinenko-Sereda theorem; 10.4 Solvability of constant-coefficient linear PDEs; Notes; 11 Fourier restriction and applications; 11.1 The Tomas-Stein theorem; 11.2 The endpoint; 11.3 Restriction and PDE; Strichartz estimates; 11.4 Optimal two-dimensional restriction; Notes; 12 Introduction to the Weyl calculus; 12.1 Motivation, definitions, basic properties; 12.2 Adjoints and compositions; 12.3 The L2 theory; 12.4 A phase-space transform; Notes; References; Index Harmonic analysis. http://id.loc.gov/authorities/subjects/sh85058939 Analyse harmonique. MATHEMATICS Mathematical Analysis. bisacsh MATHEMATICS Infinity. bisacsh Harmonic analysis fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85058939 |
| title | Classical and multilinear harmonic analysis. |
| title_auth | Classical and multilinear harmonic analysis. |
| title_exact_search | Classical and multilinear harmonic analysis. |
| title_full | Classical and multilinear harmonic analysis. Vol. 1 / Camil Muscalu and Wilhelm Schlag. |
| title_fullStr | Classical and multilinear harmonic analysis. Vol. 1 / Camil Muscalu and Wilhelm Schlag. |
| title_full_unstemmed | Classical and multilinear harmonic analysis. Vol. 1 / Camil Muscalu and Wilhelm Schlag. |
| title_short | Classical and multilinear harmonic analysis. |
| title_sort | classical and multilinear harmonic analysis |
| topic | Harmonic analysis. http://id.loc.gov/authorities/subjects/sh85058939 Analyse harmonique. MATHEMATICS Mathematical Analysis. bisacsh MATHEMATICS Infinity. bisacsh Harmonic analysis fast |
| topic_facet | Harmonic analysis. Analyse harmonique. MATHEMATICS Mathematical Analysis. MATHEMATICS Infinity. Harmonic analysis |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=508258 |
| work_keys_str_mv | AT muscalucamil classicalandmultilinearharmonicanalysisvol1 AT schlagwilhelm classicalandmultilinearharmonicanalysisvol1 |