Function spaces.: Volume 1 /
This is the first part of the second revised and extended edition of a well established monograph. It is an introduction to function spaces defined in terms of differentiability and integrability classes. It provides a catalogue of various spaces and benefits as a handbook for those who use function...
Gespeichert in:
| Weitere Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin :
De Gruyter,
2013.
|
| Ausgabe: | 2nd rev. and extended ed. |
| Schriftenreihe: | De Gruyter series in nonlinear analysis and applications ;
14. |
| Schlagworte: | |
| Online-Zugang: | DE-862 DE-863 |
| Zusammenfassung: | This is the first part of the second revised and extended edition of a well established monograph. It is an introduction to function spaces defined in terms of differentiability and integrability classes. It provides a catalogue of various spaces and benefits as a handbook for those who use function spaces to study other topics such as partial differential equations. Volume 1 deals with Banach function spaces, Volume 2 with Sobolev-type spaces. |
| Beschreibung: | 1 online resource (xv, 479 pages) : illustrations |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9783110250428 311025042X 3110250411 9783110250411 |
| ISSN: | 0941-813X ; |
Internformat
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| 245 | 0 | 0 | |a Function spaces. |n Volume 1 / |c Luboš Pick [and others]. |
| 250 | |a 2nd rev. and extended ed. | ||
| 260 | |a Berlin : |b De Gruyter, |c 2013. | ||
| 300 | |a 1 online resource (xv, 479 pages) : |b illustrations | ||
| 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 De Gruyter series in nonlinear analysis and applications, |x 0941-813X ; |v 14 | |
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |a Preface; 1 Preliminaries; 1.1 Vector space; 1.2 Topological spaces; 1.3 Metric, metric space; 1.4 Norm, normed linear space; 1.5 Modular spaces; 1.6 Inner product, inner product space; 1.7 Convergence, Cauchy sequences; 1.8 Density, separability; 1.9 Completeness; 1.10 Subspaces; 1.11 Products of spaces; 1.12 Schauder bases; 1.13 Compactness; 1.14 Operators (mappings); 1.15 Isomorphism, embeddings; 1.16 Continuous linear functionals; 1.17 Dual space, weak convergence; 1.18 The principle of uniform boundedness; 1.19 Reflexivity; 1.20 Measure spaces: general extension theory. | |
| 505 | 8 | |a 1.21 The Lebesgue measure and integral1.22 Modes of convergence; 1.23 Systems of seminorms, Hahn-Saks theorem; 2 Spaces of smooth functions; 2.1 Multiindices and derivatives; 2.2 Classes of continuous and smooth functions; 2.3 Completeness; 2.4 Separability, bases; 2.5 Compactness; 2.6 Continuous linear functionals; 2.7 Extension of functions; 3 Lebesgue spaces; 3.1 Lp-classes; 3.2 Lebesgue spaces; 3.3 Mean continuity; 3.4 Mollifiers; 3.5 Density of smooth functions; 3.6 Separability; 3.7 Completeness; 3.8 The dual space; 3.9 Reflexivity; 3.10 The space L8; 3.11 Hardy inequalities. | |
| 505 | 8 | |a 6.4 Reflexivity of Banach function spaces6.5 Separability in Banach function spaces; 7 Rearrangement-invariant spaces; 7.1 Nonincreasing rearrangements; 7.2 Hardy-Littlewood inequality; 7.3 Resonant measure spaces; 7.4 Maximal nonincreasing rearrangement; 7.5 Hardy lemma; 7.6 Rearrangement-invariant spaces; 7.7 Hardy-Littlewood-Pólya principle; 7.8 Luxemburg representation theorem; 7.9 Fundamental function; 7.10 Endpoint spaces; 7.11 Almost-compact embeddings; 7.12 Gould space; 8 Lorentz spaces; 8.1 Definition and basic properties; 8.2 Embeddings between Lorentz spaces. | |
| 520 | |a This is the first part of the second revised and extended edition of a well established monograph. It is an introduction to function spaces defined in terms of differentiability and integrability classes. It provides a catalogue of various spaces and benefits as a handbook for those who use function spaces to study other topics such as partial differential equations. Volume 1 deals with Banach function spaces, Volume 2 with Sobolev-type spaces. | ||
| 546 | |a English. | ||
| 650 | 0 | |a Ideal spaces. |0 http://id.loc.gov/authorities/subjects/sh97004453 | |
| 650 | 0 | |a Sobolev spaces. |0 http://id.loc.gov/authorities/subjects/sh85123836 | |
| 650 | 0 | |a Function spaces. |0 http://id.loc.gov/authorities/subjects/sh85052310 | |
| 650 | 4 | |a Function spaces |v Congresses. | |
| 650 | 4 | |a Functional analysis. | |
| 650 | 4 | |a Mathematics. | |
| 650 | 6 | |a Espaces parfaits. | |
| 650 | 6 | |a Espaces de Sobolev. | |
| 650 | 6 | |a Espaces fonctionnels. | |
| 650 | 7 | |a MATHEMATICS |x Transformations. |2 bisacsh | |
| 650 | 7 | |a Function spaces |2 fast | |
| 650 | 7 | |a Ideal spaces |2 fast | |
| 650 | 7 | |a Sobolev spaces |2 fast | |
| 700 | 1 | |a Pick, Luboš. |0 http://id.loc.gov/authorities/names/n2013004016 | |
| 758 | |i has work: |a Volume 1 Function spaces (Text) |1 https://id.oclc.org/worldcat/entity/E39PCG6Qq4HhwJrYH4fxqrhMpq |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Kufner, Alois. |t Function Spaces, Volume 1. |d Berlin : De Gruyter, ©2012 |z 9783110250411 |
| 830 | 0 | |a De Gruyter series in nonlinear analysis and applications ; |v 14. |x 0941-813X |0 http://id.loc.gov/authorities/names/n92047842 | |
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| 880 | 8 | |6 505-00/(S |a 3.12 Sequence spaces 3.13 Modes of convergence; 3.14 Compact subsets; 3.15 Weak convergence; 3.16 Isomorphism of Lp(O) and Lp(0, μ(O)); 3.17 Schauder bases; 3.18 Weak Lebesgue spaces; 3.19 Remarks; 4 Orlicz spaces; 4.1 Introduction; 4.2 Young function, Jensen inequality; 4.3 Complementary functions; 4.4 The Δ2-condition; 4.5 Comparison of Orlicz classes; 4.6 Orlicz spaces; 4.7 Hölder inequality in Orlicz spaces; 4.8 The Luxemburg norm; 4.9 Completeness of Orlicz spaces; 4.10 Convergence in Orlicz spaces; 4.11 Separability; 4.12 The space EΦ(Ω); 4.13 Continuous linear functionals. | |
| 880 | 8 | |6 505-00/(S |a 4.14 Compact subsets of Orlicz spaces 4.15 Further properties of Orlicz spaces; 4.16 Isomorphism properties, Schauder bases; 4.17 Comparison of Orlicz spaces; 5 Morrey and Campanato spaces; 5.1 Introduction; 5.2 Marcinkiewicz spaces; 5.3 Morrey and Campanato spaces; 5.4 Completeness; 5.5 Relations to Lebesgue spaces; 5.6 Some lemmas; 5.7 Embeddings; 5.8 The John-Nirenberg space; 5.9 Another definition of the space JN(Q); 5.10 Spaces Np; λ(Q); 5.11 Miscellaneous remarks; 6 Banach function spaces; 6.1 Banach function spaces; 6.2 Associate space; 6.3 Absolute continuity of the norm. | |
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Datensatz im Suchindex
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| _version_ | 1829094954005168128 |
| adam_text | |
| any_adam_object | |
| author2 | Pick, Luboš |
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| author_facet | Pick, Luboš |
| author_sort | Pick, Luboš |
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| contents | Preface; 1 Preliminaries; 1.1 Vector space; 1.2 Topological spaces; 1.3 Metric, metric space; 1.4 Norm, normed linear space; 1.5 Modular spaces; 1.6 Inner product, inner product space; 1.7 Convergence, Cauchy sequences; 1.8 Density, separability; 1.9 Completeness; 1.10 Subspaces; 1.11 Products of spaces; 1.12 Schauder bases; 1.13 Compactness; 1.14 Operators (mappings); 1.15 Isomorphism, embeddings; 1.16 Continuous linear functionals; 1.17 Dual space, weak convergence; 1.18 The principle of uniform boundedness; 1.19 Reflexivity; 1.20 Measure spaces: general extension theory. 1.21 The Lebesgue measure and integral1.22 Modes of convergence; 1.23 Systems of seminorms, Hahn-Saks theorem; 2 Spaces of smooth functions; 2.1 Multiindices and derivatives; 2.2 Classes of continuous and smooth functions; 2.3 Completeness; 2.4 Separability, bases; 2.5 Compactness; 2.6 Continuous linear functionals; 2.7 Extension of functions; 3 Lebesgue spaces; 3.1 Lp-classes; 3.2 Lebesgue spaces; 3.3 Mean continuity; 3.4 Mollifiers; 3.5 Density of smooth functions; 3.6 Separability; 3.7 Completeness; 3.8 The dual space; 3.9 Reflexivity; 3.10 The space L8; 3.11 Hardy inequalities. 6.4 Reflexivity of Banach function spaces6.5 Separability in Banach function spaces; 7 Rearrangement-invariant spaces; 7.1 Nonincreasing rearrangements; 7.2 Hardy-Littlewood inequality; 7.3 Resonant measure spaces; 7.4 Maximal nonincreasing rearrangement; 7.5 Hardy lemma; 7.6 Rearrangement-invariant spaces; 7.7 Hardy-Littlewood-Pólya principle; 7.8 Luxemburg representation theorem; 7.9 Fundamental function; 7.10 Endpoint spaces; 7.11 Almost-compact embeddings; 7.12 Gould space; 8 Lorentz spaces; 8.1 Definition and basic properties; 8.2 Embeddings between Lorentz spaces. |
| ctrlnum | (OCoLC)834558358 |
| dewey-full | 515.73 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.73 |
| dewey-search | 515.73 |
| dewey-sort | 3515.73 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2nd rev. and extended ed. |
| format | Electronic eBook |
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3.14 Compact subsets; 3.15 Weak convergence; 3.16 Isomorphism of Lp(O) and Lp(0, μ(O)); 3.17 Schauder bases; 3.18 Weak Lebesgue spaces; 3.19 Remarks; 4 Orlicz spaces; 4.1 Introduction; 4.2 Young function, Jensen inequality; 4.3 Complementary functions; 4.4 The Δ2-condition; 4.5 Comparison of Orlicz classes; 4.6 Orlicz spaces; 4.7 Hölder inequality in Orlicz spaces; 4.8 The Luxemburg norm; 4.9 Completeness of Orlicz spaces; 4.10 Convergence in Orlicz spaces; 4.11 Separability; 4.12 The space EΦ(Ω); 4.13 Continuous linear functionals.</subfield></datafield><datafield tag="880" ind1="8" ind2=" "><subfield code="6">505-00/(S</subfield><subfield code="a">4.14 Compact subsets of Orlicz spaces 4.15 Further properties of Orlicz spaces; 4.16 Isomorphism properties, Schauder bases; 4.17 Comparison of Orlicz spaces; 5 Morrey and Campanato spaces; 5.1 Introduction; 5.2 Marcinkiewicz spaces; 5.3 Morrey and Campanato spaces; 5.4 Completeness; 5.5 Relations to Lebesgue spaces; 5.6 Some lemmas; 5.7 Embeddings; 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| id | ZDB-4-EBA-ocn834558358 |
| illustrated | Illustrated |
| indexdate | 2025-04-11T08:41:19Z |
| institution | BVB |
| isbn | 9783110250428 311025042X 3110250411 9783110250411 |
| issn | 0941-813X ; |
| language | English |
| oclc_num | 834558358 |
| open_access_boolean | |
| owner | MAIN DE-862 DE-BY-FWS DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-862 DE-BY-FWS DE-863 DE-BY-FWS |
| physical | 1 online resource (xv, 479 pages) : illustrations |
| psigel | ZDB-4-EBA FWS_PDA_EBA ZDB-4-EBA |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | De Gruyter, |
| record_format | marc |
| series | De Gruyter series in nonlinear analysis and applications ; |
| series2 | De Gruyter series in nonlinear analysis and applications, |
| spelling | Function spaces. Volume 1 / Luboš Pick [and others]. 2nd rev. and extended ed. Berlin : De Gruyter, 2013. 1 online resource (xv, 479 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier De Gruyter series in nonlinear analysis and applications, 0941-813X ; 14 Includes bibliographical references and index. Preface; 1 Preliminaries; 1.1 Vector space; 1.2 Topological spaces; 1.3 Metric, metric space; 1.4 Norm, normed linear space; 1.5 Modular spaces; 1.6 Inner product, inner product space; 1.7 Convergence, Cauchy sequences; 1.8 Density, separability; 1.9 Completeness; 1.10 Subspaces; 1.11 Products of spaces; 1.12 Schauder bases; 1.13 Compactness; 1.14 Operators (mappings); 1.15 Isomorphism, embeddings; 1.16 Continuous linear functionals; 1.17 Dual space, weak convergence; 1.18 The principle of uniform boundedness; 1.19 Reflexivity; 1.20 Measure spaces: general extension theory. 1.21 The Lebesgue measure and integral1.22 Modes of convergence; 1.23 Systems of seminorms, Hahn-Saks theorem; 2 Spaces of smooth functions; 2.1 Multiindices and derivatives; 2.2 Classes of continuous and smooth functions; 2.3 Completeness; 2.4 Separability, bases; 2.5 Compactness; 2.6 Continuous linear functionals; 2.7 Extension of functions; 3 Lebesgue spaces; 3.1 Lp-classes; 3.2 Lebesgue spaces; 3.3 Mean continuity; 3.4 Mollifiers; 3.5 Density of smooth functions; 3.6 Separability; 3.7 Completeness; 3.8 The dual space; 3.9 Reflexivity; 3.10 The space L8; 3.11 Hardy inequalities. 6.4 Reflexivity of Banach function spaces6.5 Separability in Banach function spaces; 7 Rearrangement-invariant spaces; 7.1 Nonincreasing rearrangements; 7.2 Hardy-Littlewood inequality; 7.3 Resonant measure spaces; 7.4 Maximal nonincreasing rearrangement; 7.5 Hardy lemma; 7.6 Rearrangement-invariant spaces; 7.7 Hardy-Littlewood-Pólya principle; 7.8 Luxemburg representation theorem; 7.9 Fundamental function; 7.10 Endpoint spaces; 7.11 Almost-compact embeddings; 7.12 Gould space; 8 Lorentz spaces; 8.1 Definition and basic properties; 8.2 Embeddings between Lorentz spaces. This is the first part of the second revised and extended edition of a well established monograph. It is an introduction to function spaces defined in terms of differentiability and integrability classes. It provides a catalogue of various spaces and benefits as a handbook for those who use function spaces to study other topics such as partial differential equations. Volume 1 deals with Banach function spaces, Volume 2 with Sobolev-type spaces. English. Ideal spaces. http://id.loc.gov/authorities/subjects/sh97004453 Sobolev spaces. http://id.loc.gov/authorities/subjects/sh85123836 Function spaces. http://id.loc.gov/authorities/subjects/sh85052310 Function spaces Congresses. Functional analysis. Mathematics. Espaces parfaits. Espaces de Sobolev. Espaces fonctionnels. MATHEMATICS Transformations. bisacsh Function spaces fast Ideal spaces fast Sobolev spaces fast Pick, Luboš. http://id.loc.gov/authorities/names/n2013004016 has work: Volume 1 Function spaces (Text) https://id.oclc.org/worldcat/entity/E39PCG6Qq4HhwJrYH4fxqrhMpq https://id.oclc.org/worldcat/ontology/hasWork Print version: Kufner, Alois. Function Spaces, Volume 1. Berlin : De Gruyter, ©2012 9783110250411 De Gruyter series in nonlinear analysis and applications ; 14. 0941-813X http://id.loc.gov/authorities/names/n92047842 505-00/(S 3.12 Sequence spaces 3.13 Modes of convergence; 3.14 Compact subsets; 3.15 Weak convergence; 3.16 Isomorphism of Lp(O) and Lp(0, μ(O)); 3.17 Schauder bases; 3.18 Weak Lebesgue spaces; 3.19 Remarks; 4 Orlicz spaces; 4.1 Introduction; 4.2 Young function, Jensen inequality; 4.3 Complementary functions; 4.4 The Δ2-condition; 4.5 Comparison of Orlicz classes; 4.6 Orlicz spaces; 4.7 Hölder inequality in Orlicz spaces; 4.8 The Luxemburg norm; 4.9 Completeness of Orlicz spaces; 4.10 Convergence in Orlicz spaces; 4.11 Separability; 4.12 The space EΦ(Ω); 4.13 Continuous linear functionals. 505-00/(S 4.14 Compact subsets of Orlicz spaces 4.15 Further properties of Orlicz spaces; 4.16 Isomorphism properties, Schauder bases; 4.17 Comparison of Orlicz spaces; 5 Morrey and Campanato spaces; 5.1 Introduction; 5.2 Marcinkiewicz spaces; 5.3 Morrey and Campanato spaces; 5.4 Completeness; 5.5 Relations to Lebesgue spaces; 5.6 Some lemmas; 5.7 Embeddings; 5.8 The John-Nirenberg space; 5.9 Another definition of the space JN(Q); 5.10 Spaces Np; λ(Q); 5.11 Miscellaneous remarks; 6 Banach function spaces; 6.1 Banach function spaces; 6.2 Associate space; 6.3 Absolute continuity of the norm. |
| spellingShingle | Function spaces. De Gruyter series in nonlinear analysis and applications ; Preface; 1 Preliminaries; 1.1 Vector space; 1.2 Topological spaces; 1.3 Metric, metric space; 1.4 Norm, normed linear space; 1.5 Modular spaces; 1.6 Inner product, inner product space; 1.7 Convergence, Cauchy sequences; 1.8 Density, separability; 1.9 Completeness; 1.10 Subspaces; 1.11 Products of spaces; 1.12 Schauder bases; 1.13 Compactness; 1.14 Operators (mappings); 1.15 Isomorphism, embeddings; 1.16 Continuous linear functionals; 1.17 Dual space, weak convergence; 1.18 The principle of uniform boundedness; 1.19 Reflexivity; 1.20 Measure spaces: general extension theory. 1.21 The Lebesgue measure and integral1.22 Modes of convergence; 1.23 Systems of seminorms, Hahn-Saks theorem; 2 Spaces of smooth functions; 2.1 Multiindices and derivatives; 2.2 Classes of continuous and smooth functions; 2.3 Completeness; 2.4 Separability, bases; 2.5 Compactness; 2.6 Continuous linear functionals; 2.7 Extension of functions; 3 Lebesgue spaces; 3.1 Lp-classes; 3.2 Lebesgue spaces; 3.3 Mean continuity; 3.4 Mollifiers; 3.5 Density of smooth functions; 3.6 Separability; 3.7 Completeness; 3.8 The dual space; 3.9 Reflexivity; 3.10 The space L8; 3.11 Hardy inequalities. 6.4 Reflexivity of Banach function spaces6.5 Separability in Banach function spaces; 7 Rearrangement-invariant spaces; 7.1 Nonincreasing rearrangements; 7.2 Hardy-Littlewood inequality; 7.3 Resonant measure spaces; 7.4 Maximal nonincreasing rearrangement; 7.5 Hardy lemma; 7.6 Rearrangement-invariant spaces; 7.7 Hardy-Littlewood-Pólya principle; 7.8 Luxemburg representation theorem; 7.9 Fundamental function; 7.10 Endpoint spaces; 7.11 Almost-compact embeddings; 7.12 Gould space; 8 Lorentz spaces; 8.1 Definition and basic properties; 8.2 Embeddings between Lorentz spaces. Ideal spaces. http://id.loc.gov/authorities/subjects/sh97004453 Sobolev spaces. http://id.loc.gov/authorities/subjects/sh85123836 Function spaces. http://id.loc.gov/authorities/subjects/sh85052310 Function spaces Congresses. Functional analysis. Mathematics. Espaces parfaits. Espaces de Sobolev. Espaces fonctionnels. MATHEMATICS Transformations. bisacsh Function spaces fast Ideal spaces fast Sobolev spaces fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh97004453 http://id.loc.gov/authorities/subjects/sh85123836 http://id.loc.gov/authorities/subjects/sh85052310 |
| title | Function spaces. |
| title_auth | Function spaces. |
| title_exact_search | Function spaces. |
| title_full | Function spaces. Volume 1 / Luboš Pick [and others]. |
| title_fullStr | Function spaces. Volume 1 / Luboš Pick [and others]. |
| title_full_unstemmed | Function spaces. Volume 1 / Luboš Pick [and others]. |
| title_short | Function spaces. |
| title_sort | function spaces |
| topic | Ideal spaces. http://id.loc.gov/authorities/subjects/sh97004453 Sobolev spaces. http://id.loc.gov/authorities/subjects/sh85123836 Function spaces. http://id.loc.gov/authorities/subjects/sh85052310 Function spaces Congresses. Functional analysis. Mathematics. Espaces parfaits. Espaces de Sobolev. Espaces fonctionnels. MATHEMATICS Transformations. bisacsh Function spaces fast Ideal spaces fast Sobolev spaces fast |
| topic_facet | Ideal spaces. Sobolev spaces. Function spaces. Function spaces Congresses. Functional analysis. Mathematics. Espaces parfaits. Espaces de Sobolev. Espaces fonctionnels. MATHEMATICS Transformations. Function spaces Ideal spaces Sobolev spaces |
| work_keys_str_mv | AT picklubos functionspacesvolume1 |