Littlewood - Paley and multiplier theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | Undetermined |
| Veröffentlicht: |
1977
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
Internformat
MARC
| LEADER | 00000nam a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV018794005 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | t | ||
| 008 | 040418s1977 |||| 00||| und d | ||
| 035 | |a (OCoLC)260009991 | ||
| 035 | |a (DE-599)BVBBV018794005 | ||
| 040 | |a DE-604 |b ger | ||
| 041 | |a und | ||
| 049 | |a DE-12 | ||
| 100 | 1 | |a Edwards, Robert E. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Littlewood - Paley and multiplier theory |
| 264 | 1 | |c 1977 | |
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 505 | 0 | |a Berlin [u.a.]: Springer 1977. IX,212 S. (Ergebnisse d. Mathematik u. ihrer Grenzgebiete | |
| 650 | 0 | 7 | |a Fourier-Multiplikator |0 (DE-588)4155107-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Harmonische Analyse |0 (DE-588)4023453-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Littlewood-Paley-Theorem |0 (DE-588)4352642-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Multiplikatoralgebra |0 (DE-588)4340435-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Topologische Gruppe |0 (DE-588)4135793-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Harmonische Analyse |0 (DE-588)4023453-8 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 689 | 1 | 0 | |a Littlewood-Paley-Theorem |0 (DE-588)4352642-1 |D s |
| 689 | 1 | |8 2\p |5 DE-604 | |
| 689 | 2 | 0 | |a Topologische Gruppe |0 (DE-588)4135793-0 |D s |
| 689 | 2 | |8 3\p |5 DE-604 | |
| 689 | 3 | 0 | |a Fourier-Multiplikator |0 (DE-588)4155107-2 |D s |
| 689 | 3 | |8 4\p |5 DE-604 | |
| 689 | 4 | 0 | |a Multiplikatoralgebra |0 (DE-588)4340435-2 |D s |
| 689 | 4 | |8 5\p |5 DE-604 | |
| 700 | 1 | |a Gaudry, G. I. |e Sonstige |4 oth | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=011564740&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-011564740 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 2\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 3\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 4\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 5\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 980 | 4 | |a (DE-12)AK5870744 | |
| 980 | 4 | |a (DE-12)AK07730308 | |
Datensatz im Suchindex
| _version_ | 1804131417843564544 |
|---|---|
| adam_text | Contents
Prologue 1
Chapter 1. Introduction 4
1.1. Littlewood Paley Theory for T 4
1.2. The LP and WM Properties 6
1.3. Extension of the LP and R Properties to Product Groups... 20
1.4. Intersections of Decompositions Having the LP Property... 28
Chapter 2. Convolution Operators (Scalar Valued Case) 30
2.1. Covering Families 30
2.2. The Covering Lemma 32
2.3. The Decomposition Theorem 35
2.4. Bounds for Convolution Operators 41
Chapter 3. Convolution Operators (Vector Valued Case) 50
3.1. Introduction 50
3.2. Vector Valued Functions 50
3.3. Operator Valued Kernels 52
3.4. Fourier Transforms 53
3.5. Convolution Operators 54
3.6. Bounds for Convolution Operators 55
Chapter 4. The Littlewood Paley Theorem for Certain Dis¬
connected Groups 57
4.1. The Littlewood Paley Theorem for a Class of Totally Dis¬
connected Groups 59
4.2. The Littlewood Paley Theorem for a More General Class
of Disconnected Groups 69
4.3. A Littlewood Paley Theorem for Decompositions of I
Determined by a Decreasing Sequence of Subgroups 73
Chapter 5. Martingales and the Littlewood Paley Theorem ... 76
5.1. Conditional Expectations 76
5.2. Martingales and Martingale Difference Series 80
5.3. The Littlewood Paley Theorem 91
5.4. Applications to Disconnected Groups 100
viii Contents
Chapter 6. The Theorems of M. Riesz and Steckin for U, J
andZ 104
6.1. Introduction 104
6.2. The M. Riesz, Conjugate Function, and Steckin Theorems
for R 106
6.3. The M. Riesz, Conjugate Function, and Steckin Theorems
forT Ill
6.4. The M. Riesz, Conjugate Function, and Steckin Theorems
forZ 114
6.5. The Vector Version of the M. Riesz Theorem for R, T
and 2 118
6.6. The M. Riesz Theorem for R» x T x Z 120
6.7. The Hilbert Transform 120
6.8. A Characterisation of the Hilbert Transform 128
Chapter 7. The Littlewood Paley Theorem for R, T and Z:
Dyadic Intervals 134
7.1. Introduction 134
7.2. The Littlewood Paley Theorem: First Approach 136
7.3. The Littlewood Paley Theorem: Second Approach 143
7.4. The Littlewood Paley Theorem for Finite Products of
R, T and Z: Dyadic Intervals 145
7.5. Fournier s Example 146
Chapter 8. Strong Forms of the Marcinkiewicz Multiplier
Theorem and Littlewood Paley Theorem for R, T and T... 148
8.1. Introduction 148
8.2. The Strong Marcinkiewicz Multiplier Theorem for T ... 148
8.3. The Strong Marcinkiewicz Multiplier Theorem for R ... 155
8.4. The Strong Marcinkiewicz Multiplier Theorem for Z ... 159
8.5. Decompositions which are not Hadamard 161
Chapter 9. Applications of the Littlewood Paley Theorem ... 166
9.1. Some General Results 166
9.2. Construction of A(p) Sets in Z 168
9.3. Singular Multipliers 172
Appendix A. Special Cases of the Marcinkiewicz Interpolation
Theorem 177
A.I. The Concepts of Weak Type and Strong Type 177
A.2. The Interpolation Theorems 179
A.3. Vector Valued Functions 183
Appendix B. The Homomorphism Theorem for Multipliers... 184
B.I. The Key Lemmas 184
B.2. The Homomorphism Theorem 187
Contents ix
Appendix C. Harmonic Analysis on D2 and Walsh Series on
[0, 1] 193
Appendix D. Bernstein s Inequality 197
D.I. Bernstein s Inequality for U 197
D.2. Bernstein s Inequality for T 199
D.3, Bernstein s Inequality for LCA Groups 200
Historical Notes 202
References 206
Terminology 208
Index of Notation 209
Index of Authors and Subjects 211
|
| any_adam_object | 1 |
| author | Edwards, Robert E. |
| author_facet | Edwards, Robert E. |
| author_role | aut |
| author_sort | Edwards, Robert E. |
| author_variant | r e e re ree |
| building | Verbundindex |
| bvnumber | BV018794005 |
| contents | Berlin [u.a.]: Springer 1977. IX,212 S. (Ergebnisse d. Mathematik u. ihrer Grenzgebiete |
| ctrlnum | (OCoLC)260009991 (DE-599)BVBBV018794005 |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02267nam a2200529zc 4500</leader><controlfield tag="001">BV018794005</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">040418s1977 |||| 00||| und d</controlfield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)260009991</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV018794005</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">und</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Edwards, Robert E.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Littlewood - Paley and multiplier theory</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">1977</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="505" ind1="0" ind2=" "><subfield code="a">Berlin [u.a.]: Springer 1977. IX,212 S. (Ergebnisse d. Mathematik u. ihrer Grenzgebiete</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Fourier-Multiplikator</subfield><subfield code="0">(DE-588)4155107-2</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="650" ind1="0" ind2="7"><subfield code="a">Littlewood-Paley-Theorem</subfield><subfield code="0">(DE-588)4352642-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Multiplikatoralgebra</subfield><subfield code="0">(DE-588)4340435-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Topologische Gruppe</subfield><subfield code="0">(DE-588)4135793-0</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=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Littlewood-Paley-Theorem</subfield><subfield code="0">(DE-588)4352642-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="2" ind2="0"><subfield code="a">Topologische Gruppe</subfield><subfield code="0">(DE-588)4135793-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2=" "><subfield code="8">3\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="3" ind2="0"><subfield code="a">Fourier-Multiplikator</subfield><subfield code="0">(DE-588)4155107-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="3" ind2=" "><subfield code="8">4\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="4" ind2="0"><subfield code="a">Multiplikatoralgebra</subfield><subfield code="0">(DE-588)4340435-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="4" ind2=" "><subfield code="8">5\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Gaudry, G. I.</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</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=011564740&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:BVB01-011564740</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><datafield tag="883" ind1="1" ind2=" "><subfield code="8">2\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><datafield tag="883" ind1="1" ind2=" "><subfield code="8">3\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><datafield tag="883" ind1="1" ind2=" "><subfield code="8">4\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><datafield tag="883" ind1="1" ind2=" "><subfield code="8">5\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><datafield tag="980" ind1="4" ind2=" "><subfield code="a">(DE-12)AK5870744</subfield></datafield><datafield tag="980" ind1="4" ind2=" "><subfield code="a">(DE-12)AK07730308</subfield></datafield></record></collection> |
| id | DE-604.BV018794005 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:36:36Z |
| institution | BVB |
| language | Undetermined |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-011564740 |
| oclc_num | 260009991 |
| open_access_boolean | |
| owner | DE-12 |
| owner_facet | DE-12 |
| publishDate | 1977 |
| publishDateSearch | 1977 |
| publishDateSort | 1977 |
| record_format | marc |
| spelling | Edwards, Robert E. Verfasser aut Littlewood - Paley and multiplier theory 1977 txt rdacontent n rdamedia nc rdacarrier Berlin [u.a.]: Springer 1977. IX,212 S. (Ergebnisse d. Mathematik u. ihrer Grenzgebiete Fourier-Multiplikator (DE-588)4155107-2 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Littlewood-Paley-Theorem (DE-588)4352642-1 gnd rswk-swf Multiplikatoralgebra (DE-588)4340435-2 gnd rswk-swf Topologische Gruppe (DE-588)4135793-0 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 s 1\p DE-604 Littlewood-Paley-Theorem (DE-588)4352642-1 s 2\p DE-604 Topologische Gruppe (DE-588)4135793-0 s 3\p DE-604 Fourier-Multiplikator (DE-588)4155107-2 s 4\p DE-604 Multiplikatoralgebra (DE-588)4340435-2 s 5\p DE-604 Gaudry, G. I. Sonstige oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=011564740&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 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Edwards, Robert E. Littlewood - Paley and multiplier theory Berlin [u.a.]: Springer 1977. IX,212 S. (Ergebnisse d. Mathematik u. ihrer Grenzgebiete Fourier-Multiplikator (DE-588)4155107-2 gnd Harmonische Analyse (DE-588)4023453-8 gnd Littlewood-Paley-Theorem (DE-588)4352642-1 gnd Multiplikatoralgebra (DE-588)4340435-2 gnd Topologische Gruppe (DE-588)4135793-0 gnd |
| subject_GND | (DE-588)4155107-2 (DE-588)4023453-8 (DE-588)4352642-1 (DE-588)4340435-2 (DE-588)4135793-0 |
| title | Littlewood - Paley and multiplier theory |
| title_auth | Littlewood - Paley and multiplier theory |
| title_exact_search | Littlewood - Paley and multiplier theory |
| title_full | Littlewood - Paley and multiplier theory |
| title_fullStr | Littlewood - Paley and multiplier theory |
| title_full_unstemmed | Littlewood - Paley and multiplier theory |
| title_short | Littlewood - Paley and multiplier theory |
| title_sort | littlewood paley and multiplier theory |
| topic | Fourier-Multiplikator (DE-588)4155107-2 gnd Harmonische Analyse (DE-588)4023453-8 gnd Littlewood-Paley-Theorem (DE-588)4352642-1 gnd Multiplikatoralgebra (DE-588)4340435-2 gnd Topologische Gruppe (DE-588)4135793-0 gnd |
| topic_facet | Fourier-Multiplikator Harmonische Analyse Littlewood-Paley-Theorem Multiplikatoralgebra Topologische Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=011564740&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT edwardsroberte littlewoodpaleyandmultipliertheory AT gaudrygi littlewoodpaleyandmultipliertheory |