Holdings: Analytic capacity, the cauchy transform, and non-homogeneous Calderón–Zygmund theory

Analytic capacity, the cauchy transform, and non-homogeneous Calderón–Zygmund theory:

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Bibliographic Details
Main Author:	Tolsa, Xavier (Author)
Format:	Electronic eBook
Language:	English
Published:	Cham [u.a.] Birkhäuser 2014
Series:	Progress in mathematics 307
Online Access:	BTU01 FRO01 TUM01 UBA01 UBM01 UBT01 UBW01 UPA01 Volltext Inhaltsverzeichnis Abstract
Physical Description:	1 Online-Ressource
ISBN:	9783319005959 9783319005966
DOI:	10.1007/978-3-319-00596-6

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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.
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author	Tolsa, Xavier
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dewey-ones	515 - Analysis
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dewey-sort	3515.9
dewey-tens	510 - Mathematics
discipline	Mathematik Medizin
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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
url	https://doi.org/10.1007/978-3-319-00596-6 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 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
volume_link	(DE-604)BV035421267
work_keys_str_mv	AT tolsaxavier analyticcapacitythecauchytransformandnonhomogeneouscalderonzygmundtheory

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