Singular integrals and differentiability properties of functions:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Princeton, NJ
Princeton University Press
1986
|
| Edition: | fifth printing, with corrections |
| Series: | Princeton mathematical series
30 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XIV, 287 Seiten |
| ISBN: | 0691080798 9780691080796 |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV010221673 | ||
| 003 | DE-604 | ||
| 005 | 20200724 | ||
| 007 | t | ||
| 008 | 950614s1986 |||| 00||| engod | ||
| 020 | |a 0691080798 |9 0-691-08079-8 | ||
| 020 | |a 9780691080796 |9 978-0-691-08079-6 | ||
| 035 | |a (OCoLC)16785221 | ||
| 035 | |a (DE-599)BVBBV010221673 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-91G |a DE-92 |a DE-355 |a DE-19 |a DE-706 |a DE-634 |a DE-11 |a DE-188 |a DE-29T | ||
| 050 | 0 | |a QA331.5 | |
| 082 | 0 | |a 515.82433 | |
| 082 | 0 | |a 515/.82/433 | |
| 084 | |a SK 450 |0 (DE-625)143240: |2 rvk | ||
| 084 | |a MAT 263f |2 stub | ||
| 100 | 1 | |a Stein, Elias M. |d 1931-2018 |e Verfasser |0 (DE-588)119278596 |4 aut | |
| 245 | 1 | 0 | |a Singular integrals and differentiability properties of functions |c Elias M. Stein |
| 250 | |a fifth printing, with corrections | ||
| 264 | 1 | |a Princeton, NJ |b Princeton University Press |c 1986 | |
| 300 | |a XIV, 287 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Princeton mathematical series |v 30 | |
| 490 | 0 | |a Princeton landmarks in mathematics | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 4 | |a Fonksiyonlar, Reel değişkenli | |
| 650 | 4 | |a Harmonik analiz | |
| 650 | 4 | |a Tekil integraller | |
| 650 | 4 | |a Functions of real variables | |
| 650 | 4 | |a Harmonic analysis | |
| 650 | 4 | |a Singular integrals | |
| 650 | 0 | 7 | |a Singuläres Integral |0 (DE-588)4181533-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Integraltransformation |0 (DE-588)4027235-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Differenzierbarkeit |0 (DE-588)4149807-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Harmonische Analyse |0 (DE-588)4023453-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Harmonische Analyse |0 (DE-588)4023453-8 |D s |
| 689 | 0 | 1 | |a Differenzierbarkeit |0 (DE-588)4149807-0 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Harmonische Analyse |0 (DE-588)4023453-8 |D s |
| 689 | 1 | 1 | |a Singuläres Integral |0 (DE-588)4181533-6 |D s |
| 689 | 1 | |5 DE-604 | |
| 689 | 2 | 0 | |a Integraltransformation |0 (DE-588)4027235-7 |D s |
| 689 | 2 | |8 1\p |5 DE-604 | |
| 830 | 0 | |a Princeton mathematical series |v 30 |w (DE-604)BV000019035 |9 30 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006793164&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-006793164 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Record in the Search Index
| _version_ | 1804124631140925440 |
|---|---|
| adam_text | Contents
Preface vii
Notation
ix
I. Some Fundamental Notions of Real-Variable Theory
3
1.
The maximal function
4
2.
Behavior near general points of measurable sets
12
3.
Decomposition in cubes of open sets in R
16
4.
An interpolation theorem for L
20
5.
Further results
22
II. Singular Integrals
26
1.
Review of certain aspects of harmonic analysis in R
27
2.
Singular integrals: the heart of the matter
28
3.
Singular integrals: some extensions and variants of the
preceding
34
4.
Singular integral operators which commute with dilations
38
5.
Vector-valued analogues
45
6.
Further results
48
III. Riesz Transforms,
Poisson
Integrals, and Spherical
Harmonics
54
1.
The Riesz transforms
54
2.
Poisson
integrals and approximations to the identity
60
3.
Higher Riesz transforms and spherical harmonics
68
4.
Further results
77
IV. The Littlewood-Paley Theory and Multipliers
81
1.
The Littlewood-Paley ¿--function
82
2.
The function g*
86
3.
Multipliers (first version)
94
xiii
XIV CONTENTS
4.
Application of the partial sums operators
99
5.
The dyadic decomposition
103
6.
The Marcinkiewicz multiplier theorem
108
7.
Further results
112
V. Differentiability Properties in Terms of Function Spaces
116
1.
Riesz potentials
117
2.
The Sobolev spaces, ¿»(R )
121
3.
Bessel potentials
130
4.
The spaces
Ля
of Lipschitz continuous functions
141
5.
The spaces
Λ*·«
150
6.
Further results
159
VI. Extensions and Restrictions
166
1.
Decomposition of open sets into cubes
167
2.
Extension theorems of Whitney type
170
3.
Extension theorem for a domain with minimally smooth
boundary
180
4.
Further results
192
VII.
Return to the Theory of Harmonic Functions
196
1.
Non-tangential convergence and Fatou s theorem
196
2.
The area integral
205
3.
Application of the theory of H spaces
217
4.
Further results
235
VIII.
Differentiation of Functions
240
1.
Several notions of pointwise differentiability
241
2.
The splitting of functions
246
3.
A characterization of differentiability
250
4.
Desymmetrization principle
257
5.
Another characterization of differentiability
262
6.
Further results
266
Appendices
A. Some Inequalities
271
B. The Marcinkiewicz Interpolation Theorem
272
С
Some Elementary Properties of Harmonic Functions
274
D. Inequalities for Rademacher Functions
276
Bibliography
279
Index
289
|
| any_adam_object | 1 |
| author | Stein, Elias M. 1931-2018 |
| author_GND | (DE-588)119278596 |
| author_facet | Stein, Elias M. 1931-2018 |
| author_role | aut |
| author_sort | Stein, Elias M. 1931-2018 |
| author_variant | e m s em ems |
| building | Verbundindex |
| bvnumber | BV010221673 |
| callnumber-first | Q - Science |
| callnumber-label | QA331 |
| callnumber-raw | QA331.5 |
| callnumber-search | QA331.5 |
| callnumber-sort | QA 3331.5 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 450 |
| classification_tum | MAT 263f |
| ctrlnum | (OCoLC)16785221 (DE-599)BVBBV010221673 |
| dewey-full | 515.82433 515/.82/433 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.82433 515/.82/433 |
| dewey-search | 515.82433 515/.82/433 |
| dewey-sort | 3515.82433 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | fifth printing, with corrections |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02554nam a2200625 cb4500</leader><controlfield tag="001">BV010221673</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20200724 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">950614s1986 |||| 00||| engod</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0691080798</subfield><subfield code="9">0-691-08079-8</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780691080796</subfield><subfield code="9">978-0-691-08079-6</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)16785221</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV010221673</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-91G</subfield><subfield code="a">DE-92</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-706</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-29T</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA331.5</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515.82433</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515/.82/433</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 450</subfield><subfield code="0">(DE-625)143240:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 263f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Stein, Elias M.</subfield><subfield code="d">1931-2018</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)119278596</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Singular integrals and differentiability properties of functions</subfield><subfield code="c">Elias M. Stein</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">fifth printing, with corrections</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Princeton, NJ</subfield><subfield code="b">Princeton University Press</subfield><subfield code="c">1986</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XIV, 287 Seiten</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Princeton mathematical series</subfield><subfield code="v">30</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Princeton landmarks in mathematics</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Hier auch später erschienene, unveränderte Nachdrucke</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Fonksiyonlar, Reel değişkenli</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Harmonik analiz</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Tekil integraller</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Functions of real variables</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Harmonic analysis</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Singular integrals</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Singuläres Integral</subfield><subfield code="0">(DE-588)4181533-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Integraltransformation</subfield><subfield code="0">(DE-588)4027235-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Differenzierbarkeit</subfield><subfield code="0">(DE-588)4149807-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Harmonische Analyse</subfield><subfield code="0">(DE-588)4023453-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Harmonische Analyse</subfield><subfield code="0">(DE-588)4023453-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Differenzierbarkeit</subfield><subfield code="0">(DE-588)4149807-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Harmonische Analyse</subfield><subfield code="0">(DE-588)4023453-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Singuläres Integral</subfield><subfield code="0">(DE-588)4181533-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="2" ind2="0"><subfield code="a">Integraltransformation</subfield><subfield code="0">(DE-588)4027235-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Princeton mathematical series</subfield><subfield code="v">30</subfield><subfield code="w">(DE-604)BV000019035</subfield><subfield code="9">30</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Regensburg</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006793164&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-006793164</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| id | DE-604.BV010221673 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:48:44Z |
| institution | BVB |
| isbn | 0691080798 9780691080796 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006793164 |
| oclc_num | 16785221 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-92 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-706 DE-634 DE-11 DE-188 DE-29T |
| owner_facet | DE-91G DE-BY-TUM DE-92 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-706 DE-634 DE-11 DE-188 DE-29T |
| physical | XIV, 287 Seiten |
| publishDate | 1986 |
| publishDateSearch | 1986 |
| publishDateSort | 1986 |
| publisher | Princeton University Press |
| record_format | marc |
| series | Princeton mathematical series |
| series2 | Princeton mathematical series Princeton landmarks in mathematics |
| spelling | Stein, Elias M. 1931-2018 Verfasser (DE-588)119278596 aut Singular integrals and differentiability properties of functions Elias M. Stein fifth printing, with corrections Princeton, NJ Princeton University Press 1986 XIV, 287 Seiten txt rdacontent n rdamedia nc rdacarrier Princeton mathematical series 30 Princeton landmarks in mathematics Hier auch später erschienene, unveränderte Nachdrucke Fonksiyonlar, Reel değişkenli Harmonik analiz Tekil integraller Functions of real variables Harmonic analysis Singular integrals Singuläres Integral (DE-588)4181533-6 gnd rswk-swf Integraltransformation (DE-588)4027235-7 gnd rswk-swf Differenzierbarkeit (DE-588)4149807-0 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 s Differenzierbarkeit (DE-588)4149807-0 s DE-604 Singuläres Integral (DE-588)4181533-6 s Integraltransformation (DE-588)4027235-7 s 1\p DE-604 Princeton mathematical series 30 (DE-604)BV000019035 30 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006793164&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Stein, Elias M. 1931-2018 Singular integrals and differentiability properties of functions Princeton mathematical series Fonksiyonlar, Reel değişkenli Harmonik analiz Tekil integraller Functions of real variables Harmonic analysis Singular integrals Singuläres Integral (DE-588)4181533-6 gnd Integraltransformation (DE-588)4027235-7 gnd Differenzierbarkeit (DE-588)4149807-0 gnd Harmonische Analyse (DE-588)4023453-8 gnd |
| subject_GND | (DE-588)4181533-6 (DE-588)4027235-7 (DE-588)4149807-0 (DE-588)4023453-8 |
| title | Singular integrals and differentiability properties of functions |
| title_auth | Singular integrals and differentiability properties of functions |
| title_exact_search | Singular integrals and differentiability properties of functions |
| title_full | Singular integrals and differentiability properties of functions Elias M. Stein |
| title_fullStr | Singular integrals and differentiability properties of functions Elias M. Stein |
| title_full_unstemmed | Singular integrals and differentiability properties of functions Elias M. Stein |
| title_short | Singular integrals and differentiability properties of functions |
| title_sort | singular integrals and differentiability properties of functions |
| topic | Fonksiyonlar, Reel değişkenli Harmonik analiz Tekil integraller Functions of real variables Harmonic analysis Singular integrals Singuläres Integral (DE-588)4181533-6 gnd Integraltransformation (DE-588)4027235-7 gnd Differenzierbarkeit (DE-588)4149807-0 gnd Harmonische Analyse (DE-588)4023453-8 gnd |
| topic_facet | Fonksiyonlar, Reel değişkenli Harmonik analiz Tekil integraller Functions of real variables Harmonic analysis Singular integrals Singuläres Integral Integraltransformation Differenzierbarkeit Harmonische Analyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006793164&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000019035 |
| work_keys_str_mv | AT steineliasm singularintegralsanddifferentiabilitypropertiesoffunctions |