Sobolev, Besov and Triebel-Lizorkin spaces on quantum tori:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
March 2018
|
| Series: | Memoirs of the American Mathematical Society
volume 252, number 1203 (fourth of 6 numbers) |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | vi, 118, 4 ungezählte Seiten |
| ISBN: | 9781470428068 |
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MARC
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| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c March 2018 | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Chapter 0- Introduction 1
Basic properties 3
Embedding 4
Characterizations 4
Interpolation 6
Multipliers 6
Chapter 1. Preliminaries 9
1.1. Noncommutative Lp-spaces 9
1.2. Quantum tori 10
1.3. Fourier multipliers 12
1.4. Hardy spaces 14
Chapter 2. Sobolev spaces 19
2.1. Distributions on quantum tori 19
2.2. Definitions and basic properties 21
2.3. A Poincare-type inequality 25
2.4. Lipschitz classes 28
2.5. The link with the classical Sobolev spaces 31
Chapter 3. Besov spaces 35
3.1. Definitions and basic properties 35
3.2. A general characterization 42
3.3. The characterizations by Poisson and heat semigroups 48
3.4. The characterization by differences 51
3.5. Limits of Besov norms 54
3.6. The link with the classical Besov spaces 55
Chapter 4. Triebel-Lizorkin spaces 59
4.1. A multiplier theorem 59
4.2. Definitions and basic properties 68
4.3. A general characterization 72
4.4. Concrete characterizations 76
4.5. Operator-valued Triebel-Lizorkin spaces 80
Chapter 5. Interpolation 83
5.1. Interpolation of Besov and Sobolev spaces 83
5.2. The K-functional of (Z/p, W£) 88
5.3. Interpolation of Triebel-Lizorkin spaces 91
iii
IV
CONTENTS
Chapter 6. Embedding 93
6.1. Embedding of Besov spaces 93
6.2. Embedding of Sobolev spaces 95
6.3. Compact embedding 100
Chapter 7. Fourier multiplier 103
7.1. Fourier multipliers on Sobolev spaces 103
7.2. Fourier multipliers on Besov spaces 107
7.3. Fourier multipliers on Triebel-Lizorkin spaces 110
Acknowledgements 113
Bibliography 115
|
| any_adam_object | 1 |
| author | Xiong, Xiao Xu, Quanhua Yin, Zhi |
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| id | DE-604.BV044905883 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T08:04:23Z |
| institution | BVB |
| isbn | 9781470428068 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030299554 |
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| owner_facet | DE-83 DE-355 DE-BY-UBR DE-29T DE-11 |
| physical | vi, 118, 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 |
| spelling | Xiong, Xiao aut Sobolev, Besov and Triebel-Lizorkin spaces on quantum tori Xiao Xiong ; Quanhua Xu ; Zhi Yin Providence, Rhode Island American Mathematical Society March 2018 vi, 118, 4 ungezählte Seiten txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society volume 252, number 1203 (fourth of 6 numbers) Torus (DE-588)4185738-0 gnd rswk-swf Lipschitz-Raum (DE-588)4431681-1 gnd rswk-swf Sobolev-Raum (DE-588)4055345-0 gnd rswk-swf Sobolev-Raum (DE-588)4055345-0 s Lipschitz-Raum (DE-588)4431681-1 s Torus (DE-588)4185738-0 s 1\p DE-604 Xu, Quanhua aut Yin, Zhi aut Memoirs of the American Mathematical Society volume 252, number 1203 (fourth of 6 numbers) (DE-604)BV008000141 1203 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030299554&sequence=000001&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 | Xiong, Xiao Xu, Quanhua Yin, Zhi Sobolev, Besov and Triebel-Lizorkin spaces on quantum tori Memoirs of the American Mathematical Society Torus (DE-588)4185738-0 gnd Lipschitz-Raum (DE-588)4431681-1 gnd Sobolev-Raum (DE-588)4055345-0 gnd |
| subject_GND | (DE-588)4185738-0 (DE-588)4431681-1 (DE-588)4055345-0 |
| title | Sobolev, Besov and Triebel-Lizorkin spaces on quantum tori |
| title_auth | Sobolev, Besov and Triebel-Lizorkin spaces on quantum tori |
| title_exact_search | Sobolev, Besov and Triebel-Lizorkin spaces on quantum tori |
| title_full | Sobolev, Besov and Triebel-Lizorkin spaces on quantum tori Xiao Xiong ; Quanhua Xu ; Zhi Yin |
| title_fullStr | Sobolev, Besov and Triebel-Lizorkin spaces on quantum tori Xiao Xiong ; Quanhua Xu ; Zhi Yin |
| title_full_unstemmed | Sobolev, Besov and Triebel-Lizorkin spaces on quantum tori Xiao Xiong ; Quanhua Xu ; Zhi Yin |
| title_short | Sobolev, Besov and Triebel-Lizorkin spaces on quantum tori |
| title_sort | sobolev besov and triebel lizorkin spaces on quantum tori |
| topic | Torus (DE-588)4185738-0 gnd Lipschitz-Raum (DE-588)4431681-1 gnd Sobolev-Raum (DE-588)4055345-0 gnd |
| topic_facet | Torus Lipschitz-Raum Sobolev-Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030299554&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
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