Analytic capacity, the cauchy transform, and non-homogeneous Calderón–Zygmund theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cham [u.a.]
Birkhäuser
2014
|
| Schriftenreihe: | Progress in mathematics
307 |
| Online-Zugang: | BTU01 FRO01 TUM01 UBA01 UBM01 UBT01 UBW01 UPA01 Volltext Inhaltsverzeichnis Abstract |
| Beschreibung: | 1 Online-Ressource |
| ISBN: | 9783319005959 9783319005966 |
| DOI: | 10.1007/978-3-319-00596-6 |
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Datensatz im Suchindex
| _version_ | 1804151869584441344 |
|---|---|
| adam_text | ANALYTIC CAPACITY, THE CAUCHY TRANSFORM, AND NON-HOMOGENEOUS
CALDERON–ZYGMUND THEORY
/ TOLSA, XAVIER
: 2014
TABLE OF CONTENTS / INHALTSVERZEICHNIS
INTRODUCTION
BASIC NOTATION
CHAPTER 1. ANALYTIC CAPACITY
CHAPTER 2. BASIC CALDERON-ZYGMUND THEORY WITH NON DOUBLING MEASURES
CHAPTER 3. THE CAUCHY TRANSFORM AND MENGER CURVATURE
CHAPTER 4. THE CAPACITY Γ+
CHAPTER 5. A TB THEOREM OF NAZAROV, TREIL AND VOLBERG
CHAPTER 6. THE COMPARABILITY BETWEEN Γ AND Γ +, AND THE SEMIADDITIVITY
OF ANALYTIC CAPACITY
CHAPTER 7. CURVATURE AND RECTIFIABILITY
CHAPTER 8. PRINCIPAL VALUES FOR THE CAUCHY TRANSFORM AND RECTIFIABILITY
CHAPTER 9. RBMO(Μ) AND H1 ATB(Μ)
BIBLIOGRAPHY
INDEX
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
ANALYTIC CAPACITY, THE CAUCHY TRANSFORM, AND NON-HOMOGENEOUS
CALDERON–ZYGMUND THEORY
/ TOLSA, XAVIER
: 2014
ABSTRACT / INHALTSTEXT
THIS BOOK STUDIES SOME OF THE GROUNDBREAKING ADVANCES THAT HAVE BEEN
MADE REGARDING ANALYTIC CAPACITY AND ITS RELATIONSHIP TO RECTIFIABILITY
IN THE DECADE 1995–2005. THE CAUCHY TRANSFORM PLAYS A FUNDAMENTAL ROLE
IN THIS AREA AND IS ACCORDINGLY ONE OF THE MAIN SUBJECTS COVERED.
ANOTHER IMPORTANT TOPIC, WHICH MAY BE OF INDEPENDENT INTEREST FOR MANY
ANALYSTS, IS THE SO-CALLED NON-HOMOGENEOUS CALDERON-ZYGMUND THEORY, THE
DEVELOPMENT OF WHICH HAS BEEN LARGELY MOTIVATED BY THE PROBLEMS ARISING
IN CONNECTION WITH ANALYTIC CAPACITY. THE PAINLEVE PROBLEM, WHICH WAS
FIRST POSED AROUND 1900, CONSISTS IN FINDING A DESCRIPTION OF THE
REMOVABLE SINGULARITIES FOR BOUNDED ANALYTIC FUNCTIONS IN METRIC AND
GEOMETRIC TERMS. ANALYTIC CAPACITY IS A KEY TOOL IN THE STUDY OF THIS
PROBLEM. IN THE 1960S VITUSHKIN CONJECTURED THAT THE REMOVABLE SETS
WHICH HAVE FINITE LENGTH COINCIDE WITH THOSE WHICH ARE PURELY
UNRECTIFIABLE. MOREOVER, BECAUSE OF THE APPLICATIONS TO THE THEORY OF
UNIFORM RATIONAL APPROXIMATION, HE POSED THE QUESTION AS TO WHETHER
ANALYTIC CAPACITY IS SEMIADDITIVE. THIS WORK PRESENTS FULL PROOFS OF
VITUSHKIN’S CONJECTURE AND OF THE SEMIADDITIVITY OF ANALYTIC CAPACITY,
BOTH OF WHICH REMAINED OPEN PROBLEMS UNTIL VERY RECENTLY. OTHER RELATED
QUESTIONS ARE ALSO DISCUSSED, SUCH AS THE RELATIONSHIP BETWEEN
RECTIFIABILITY AND THE EXISTENCE OF PRINCIPAL VALUES FOR THE CAUCHY
TRANSFORMS AND OTHER SINGULAR INTEGRALS. THE BOOK IS LARGELY
SELF-CONTAINED AND SHOULD BE ACCESSIBLE FOR GRADUATE STUDENTS IN
ANALYSIS, AS WELL AS A VALUABLE RESOURCE FOR RESEARCHERS
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
| any_adam_object | 1 |
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| spelling | Tolsa, Xavier Verfasser aut Analytic capacity, the cauchy transform, and non-homogeneous Calderón–Zygmund theory Xavier Tolsa Cham [u.a.] Birkhäuser 2014 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Progress in mathematics 307 Progress in mathematics 307 (DE-604)BV035421267 307 https://doi.org/10.1007/978-3-319-00596-6 Verlag Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027085499&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027085499&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Abstract |
| spellingShingle | Tolsa, Xavier Analytic capacity, the cauchy transform, and non-homogeneous Calderón–Zygmund theory Progress in mathematics |
| title | Analytic capacity, the cauchy transform, and non-homogeneous Calderón–Zygmund theory |
| title_auth | Analytic capacity, the cauchy transform, and non-homogeneous Calderón–Zygmund theory |
| title_exact_search | Analytic capacity, the cauchy transform, and non-homogeneous Calderón–Zygmund theory |
| title_full | Analytic capacity, the cauchy transform, and non-homogeneous Calderón–Zygmund theory Xavier Tolsa |
| title_fullStr | Analytic capacity, the cauchy transform, and non-homogeneous Calderón–Zygmund theory Xavier Tolsa |
| title_full_unstemmed | Analytic capacity, the cauchy transform, and non-homogeneous Calderón–Zygmund theory Xavier Tolsa |
| title_short | Analytic capacity, the cauchy transform, and non-homogeneous Calderón–Zygmund theory |
| title_sort | analytic capacity the cauchy transform and non homogeneous calderon zygmund theory |
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