Hardy spaces and potential theory on C1 domains in Riemannian manifolds:
The author studies Hardy spaces on C1 and Lipschitz domains in Riemannian manifolds. Hardy spaces, originally introduced in 1920 in complex analysis setting, are invaluable tool in harmonic analysis. For this reason these spaces have been studied extensively by many authors.
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Mathematical Society
2008
|
| Series: | Memoirs of the American Mathematical Society
894 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | The author studies Hardy spaces on C1 and Lipschitz domains in Riemannian manifolds. Hardy spaces, originally introduced in 1920 in complex analysis setting, are invaluable tool in harmonic analysis. For this reason these spaces have been studied extensively by many authors. |
| Item Description: | "Volume 191, number 894 (fourth of 5 numbers)." Includes bibliographical references |
| Physical Description: | VI, 78 S. |
| ISBN: | 9780821840436 |
Staff View
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| adam_text | I /R EMOIRS -L * X. OF THE AMERICAN MATHEMATICAL SOCIETY NUMBER 894
HARDY SPACES AND POTENTIAL THEORY ON C 1 DOMAINS IN RIEMANNIAN MANIFOLDS
MARTIN DINDOS JANUARY 2008 * VOLUME 191 * NUMBER 894 (FOURTH OF 5
NUMBERS) * ISSN 0065-9266 AMERICAN MATHEMATICAL SOCIETY PROVIDENCE,
RHODE ISLAND CONTENTS ABSTRACT VI CHAPTER 0. INTRODUCTION 1 CHAPTER 1.
BACKGROUND AND DEFINITIONS 4 §1.1. NOTATION, TERMINOLOGY AND KNOWN
RESULTS 4 §1.2. HARDY SPACES AND LAYER POTENTIALS 6 CHAPTER 2. THE
BOUNDARY LAYER POTENTIALS 9 §2.1. COMPACTNESS OF OPERATORS K, K* 9 §2.2.
INVERTIBILITY OF L + K, L + K* 19 CHAPTER 3. THE DIRICHLET PROBLEM
21 §3.1. W BOUNDARY DATA 21 §3.2. HARDY SPACE BOUNDARY DATA 23 §3.3.
HOLDER SPACE BOUNDARY DATA 25 CHAPTER 4. THE NEUMANN PROBLEM 27 §4.1. LP
BOUNDARY DATA 27 §4.2. HARDY SPACE BOUNDARY DATA 27 §4.3. HOLDER SPACE
BOUNDARY DATA 29 CHAPTER 5. COMPACTNESS OF LAYER POTENTIALS, PART II;
THE DIRICHLET REGU- LARITY PROBLEM 31 §5.1. PRELIMINARIES 31 §5.2.
COMPACTNESS AND INVERTIBILITY OF K ON SOBOLEV SPACE H L P 33 §5.3.
COMPACTNESS AND INVERTIBILITY OF K ON HARDY-SOBOLEV SPACE H 1 38 §5.4.
DIRICHLET REGULARITY PROBLEM, SOBOLEV H 1 (1 P OO) DATA 41 §5.5.
DIRICHLET REGULARITY PROBLEM, H L P ((N - L)/N P 1) DATA 42
CHAPTER 6. THE EQUIVALENCE OF HARDY SPACE DEFINITIONS 44 §6.1.
PRELIMINARIES 44 §6.2. C-SUHARMONICITY 45 §6.3. THE MAIN STEP 47 §6.4.
THE EQUIVALENCE THEOREM ON C 1 DOMAINS 50 §6.5. THE EQUIVALENCE THEOREM
ON LIPSCHITZ DOMAINS 51 APPENDIX A. VARIABLE COEFFICIENT CAUCHY
INTEGRALS 53 APPENDIX B. ONE RESULT ON THE MAXIMAL OPERATOR 65
BIBLIOGRAPHY 77
|
| adam_txt |
I\/R EMOIRS -L * X. OF THE AMERICAN MATHEMATICAL SOCIETY NUMBER 894
HARDY SPACES AND POTENTIAL THEORY ON C 1 DOMAINS IN RIEMANNIAN MANIFOLDS
MARTIN DINDOS JANUARY 2008 * VOLUME 191 * NUMBER 894 (FOURTH OF 5
NUMBERS) * ISSN 0065-9266 AMERICAN MATHEMATICAL SOCIETY PROVIDENCE,
RHODE ISLAND CONTENTS ABSTRACT VI CHAPTER 0. INTRODUCTION 1 CHAPTER 1.
BACKGROUND AND DEFINITIONS 4 §1.1. NOTATION, TERMINOLOGY AND KNOWN
RESULTS 4 §1.2. HARDY SPACES AND LAYER POTENTIALS 6 CHAPTER 2. THE
BOUNDARY LAYER POTENTIALS 9 §2.1. COMPACTNESS OF OPERATORS K, K* 9 §2.2.
INVERTIBILITY OF \L + K, \L + K* 19 CHAPTER 3. THE DIRICHLET PROBLEM
21 §3.1. W BOUNDARY DATA 21 §3.2. HARDY SPACE BOUNDARY DATA 23 §3.3.
HOLDER SPACE BOUNDARY DATA 25 CHAPTER 4. THE NEUMANN PROBLEM 27 §4.1. LP
BOUNDARY DATA 27 §4.2. HARDY SPACE BOUNDARY DATA 27 §4.3. HOLDER SPACE
BOUNDARY DATA 29 CHAPTER 5. COMPACTNESS OF LAYER POTENTIALS, PART II;
THE DIRICHLET REGU- LARITY PROBLEM 31 §5.1. PRELIMINARIES 31 §5.2.
COMPACTNESS AND INVERTIBILITY OF K ON SOBOLEV SPACE H L ' P 33 §5.3.
COMPACTNESS AND INVERTIBILITY OF K ON HARDY-SOBOLEV SPACE H 1 38 §5.4.
DIRICHLET REGULARITY PROBLEM, SOBOLEV H 1 (1 P OO) DATA 41 §5.5.
DIRICHLET REGULARITY PROBLEM, H L ' P ((N - L)/N P 1) DATA 42
CHAPTER 6. THE EQUIVALENCE OF HARDY SPACE DEFINITIONS 44 §6.1.
PRELIMINARIES 44 §6.2. C-SUHARMONICITY 45 §6.3. THE MAIN STEP 47 §6.4.
THE EQUIVALENCE THEOREM ON C 1 DOMAINS 50 §6.5. THE EQUIVALENCE THEOREM
ON LIPSCHITZ DOMAINS 51 APPENDIX A. VARIABLE COEFFICIENT CAUCHY
INTEGRALS 53 APPENDIX B. ONE RESULT ON THE MAXIMAL OPERATOR 65
BIBLIOGRAPHY 77 |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T19:57:53Z |
| indexdate | 2024-07-09T21:12:13Z |
| institution | BVB |
| isbn | 9780821840436 |
| language | English |
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| physical | VI, 78 S. |
| publishDate | 2008 |
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| spelling | Dindoš, Martin Verfasser aut Hardy spaces and potential theory on C1 domains in Riemannian manifolds Martin Dindoš Providence, RI American Mathematical Society 2008 VI, 78 S. txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society 894 "Volume 191, number 894 (fourth of 5 numbers)." Includes bibliographical references The author studies Hardy spaces on C1 and Lipschitz domains in Riemannian manifolds. Hardy spaces, originally introduced in 1920 in complex analysis setting, are invaluable tool in harmonic analysis. For this reason these spaces have been studied extensively by many authors. Hardy spaces Riemannian manifolds Potential theory (Mathematics) Hardy-Raum (DE-588)4159109-4 gnd rswk-swf Potenzialtheorie (DE-588)4046939-6 gnd rswk-swf Riemannscher Raum (DE-588)4128295-4 gnd rswk-swf Hardy-Raum (DE-588)4159109-4 s Riemannscher Raum (DE-588)4128295-4 s Potenzialtheorie (DE-588)4046939-6 s DE-604 Memoirs of the American Mathematical Society 894 (DE-604)BV008000141 894 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016358171&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dindoš, Martin Hardy spaces and potential theory on C1 domains in Riemannian manifolds Memoirs of the American Mathematical Society Hardy spaces Riemannian manifolds Potential theory (Mathematics) Hardy-Raum (DE-588)4159109-4 gnd Potenzialtheorie (DE-588)4046939-6 gnd Riemannscher Raum (DE-588)4128295-4 gnd |
| subject_GND | (DE-588)4159109-4 (DE-588)4046939-6 (DE-588)4128295-4 |
| title | Hardy spaces and potential theory on C1 domains in Riemannian manifolds |
| title_auth | Hardy spaces and potential theory on C1 domains in Riemannian manifolds |
| title_exact_search | Hardy spaces and potential theory on C1 domains in Riemannian manifolds |
| title_exact_search_txtP | Hardy spaces and potential theory on C1 domains in Riemannian manifolds |
| title_full | Hardy spaces and potential theory on C1 domains in Riemannian manifolds Martin Dindoš |
| title_fullStr | Hardy spaces and potential theory on C1 domains in Riemannian manifolds Martin Dindoš |
| title_full_unstemmed | Hardy spaces and potential theory on C1 domains in Riemannian manifolds Martin Dindoš |
| title_short | Hardy spaces and potential theory on C1 domains in Riemannian manifolds |
| title_sort | hardy spaces and potential theory on c1 domains in riemannian manifolds |
| topic | Hardy spaces Riemannian manifolds Potential theory (Mathematics) Hardy-Raum (DE-588)4159109-4 gnd Potenzialtheorie (DE-588)4046939-6 gnd Riemannscher Raum (DE-588)4128295-4 gnd |
| topic_facet | Hardy spaces Riemannian manifolds Potential theory (Mathematics) Hardy-Raum Potenzialtheorie Riemannscher Raum |
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| work_keys_str_mv | AT dindosmartin hardyspacesandpotentialtheoryonc1domainsinriemannianmanifolds |