Algebras of singular integral operators with Kernels controlled by multiple norms:
Gespeichert in:
| Beteiligte Personen: | , , , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2018]
|
| Schriftenreihe: | Memoirs of the American Mathematical Society
volume 256, number 1230 (sixth of 6 numbers) |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030853726&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | v, 108, 4 ungezählte Seiten |
| ISBN: | 9781470434380 |
Internformat
MARC
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| 245 | 1 | 0 | |a Algebras of singular integral operators with Kernels controlled by multiple norms |c Alexander Nagel, Fulvio Ricci, Elias M.Stein, Stephen Wainger |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2018] | |
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Datensatz im Suchindex
| _version_ | 1819325129747857408 |
|---|---|
| adam_text | Contents
Chapter 1. Introduction 1
1.1. Background 1
1.2. Some motivating examples 2
1.3. Outline of results 4
Chapter 2. The Classes P(E) and A4(E) 11
2.1. Notation 11
2.2. Global norms 13
2.3. Classes of distributions and multipliers 14
Chapter 3. Marked partitions and decompositions of 17
3.1. Dominant terms in Nj(t) and Nj(t) 17
3.2. Marked partitions and the sets Es and Es 18
3.3. Characterizing the sets Eg and~E§ 19
3.4. Estimates of kernels and multipliers on Es and Es 22
3.5. A coarser decomposition of RN associated to S € S(n) 23
Chapter 4. Fourier transform duality of kernels and multipliers 25
4.1. Fourier transforms of multipliers 25
4.2. Fourier transforms of kernels 29
Chapter 5. Dyadic sums of Schwartz functions 33
5.1. Cones associated to a matrix E 33
5.2. Inclusions among classes of kernels associated to different matrices 34
5.3. Coarser decompositions and lower dimensional matrices 35
5.4. Size estimates 37
5.5. Cancellation properties 38
5.6. Dyadic sums with weak cancellation 41
Chapter 6. Decomposition of multipliers and kernels 45
6.1. New matrices Es 45
6.2. Road map for the dyadic decomposition 46
6.3. Partitions of unity 47
6.4. Dyadic decomposition of a multiplier 50
6.5. Dyadic decomposition of a kernel 52
Hi
IV
CONTENTS
Chapter 7. The rank of E and integrability at infinity 57
7.1. The rank 1 case: C alder on-Zygmund kernels 57
7.2. Higher rank and integrability at infinity 59
7.3. Higher rank and weak-type estimates near zero 61
Chapter 8. Convolution operators on homogeneous nilpotent Lie groups 63
8.1. Convolution of scaled bump functions; compatibility of dilations and
convolution 63
8.2. Automorphic flag kernels and Lp-boundedness of convolution operators 66
Chapter 9. Composition of operators 69
9.1. A preliminary decomposition 72
9.2. Reduction to the case of finite sets 72
9.3. Properties of the convolution [ips i * bPrlj 73
9.4. A further decomposition of Tz(Es) x r^(Et) 76
9.5. Fixed and free indices 79
9.6. A finer decomposition of 70lN 81
9.7. The matrix EsyT,w 82
9.8. The class P0(ESit,w) 84
9.9. Estimates for [cp j * [ip j 86
9.10. Proof of Theorem 9.2 89
Chapter 10. Convolution of Calderon-Zygmund kernels 91
10.1. Calderon-Zygmund kernels 91
10.2. A general convolution theorem 91
10.3. Convolution of two Calderon-Zygmund kernels 92
Chapter 11. Two-flag kernels and multipliers 99
11.1. Flag kernels and multipliers 99
11.2. Pairs of opposite flags 100
11.3. Two-step flags 101
11.4. General two-flag kernels 103
11.5. Proof of Lemma 11.6 106
Chapter 12. Extended kernels and operators 109
12.1. The Lp boundedness of the operators 109
12.2. The algebra of operators 112
Chapter 13. The role of pseudo-differential operators 115
13.1. The isotropic extended kernels 116
13.2. Proof of Theorem 13.1 118
13.3. The space L 121
Chapter 14. Appendix I: Properties of cones r(A) 123
14.1. Optimal inequalities and the basic hypothesis 123
14.2. Partial matrices 124
14.3. Projections 125
14.4. The dimension of T(E) 126
14.5. The reduced matrix Eb 128
CONTENTS
v
Chapter 15. Appendix II: Estimates for homogeneous norms 131
Chapter 16. Appendix III: Estimates for geometric sums 135
Bibliography 139
Index of Symbols 141
|
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| author | Nagel, Alexander Ricci, Fulvio 1948- Stein, Elias M. 1931-2018 Wainger, Stephen 1936- |
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| id | DE-604.BV045468576 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T18:27:54Z |
| institution | BVB |
| isbn | 9781470434380 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030853726 |
| oclc_num | 1088347332 |
| open_access_boolean | |
| owner | DE-83 DE-355 DE-BY-UBR DE-29T DE-11 |
| owner_facet | DE-83 DE-355 DE-BY-UBR DE-29T DE-11 |
| physical | v, 108, 4 ungezählte Seiten |
| publishDate | 2018 |
| publishDateSearch | 2018 |
| publishDateSort | 2018 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spellingShingle | Nagel, Alexander Ricci, Fulvio 1948- Stein, Elias M. 1931-2018 Wainger, Stephen 1936- Algebras of singular integral operators with Kernels controlled by multiple norms Memoirs of the American Mathematical Society Kern Mathematik (DE-588)4163599-1 gnd Algebra (DE-588)4001156-2 gnd Singulärer Integraloperator (DE-588)4131249-1 gnd Integraloperator (DE-588)4131247-8 gnd |
| subject_GND | (DE-588)4163599-1 (DE-588)4001156-2 (DE-588)4131249-1 (DE-588)4131247-8 |
| title | Algebras of singular integral operators with Kernels controlled by multiple norms |
| title_auth | Algebras of singular integral operators with Kernels controlled by multiple norms |
| title_exact_search | Algebras of singular integral operators with Kernels controlled by multiple norms |
| title_full | Algebras of singular integral operators with Kernels controlled by multiple norms Alexander Nagel, Fulvio Ricci, Elias M.Stein, Stephen Wainger |
| title_fullStr | Algebras of singular integral operators with Kernels controlled by multiple norms Alexander Nagel, Fulvio Ricci, Elias M.Stein, Stephen Wainger |
| title_full_unstemmed | Algebras of singular integral operators with Kernels controlled by multiple norms Alexander Nagel, Fulvio Ricci, Elias M.Stein, Stephen Wainger |
| title_short | Algebras of singular integral operators with Kernels controlled by multiple norms |
| title_sort | algebras of singular integral operators with kernels controlled by multiple norms |
| topic | Kern Mathematik (DE-588)4163599-1 gnd Algebra (DE-588)4001156-2 gnd Singulärer Integraloperator (DE-588)4131249-1 gnd Integraloperator (DE-588)4131247-8 gnd |
| topic_facet | Kern Mathematik Algebra Singulärer Integraloperator Integraloperator |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030853726&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
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