Analytic capacity, rectifiability, menger curvature and the cauchy integral:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Heidelberg ; New York ; Hong Kong ; London ; Milan ; Pa
Springer
2002
|
| Schriftenreihe: | Lecture notes in mathematics
1799 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 118 S. graph. Darst. |
| ISBN: | 3540000011 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804129584655892480 |
|---|---|
| adam_text | Contents
Introduction v
Notations and conventions ix
Chapter 1. Some geometric measure theory 1
1. Carleson measures 1
2. Lipschitz maps 2
3. Hausdorff dimension and HausdorfT measures 4
4. Density properties of Hausdorff measures 7
5. Rectifiable and purely unrectifiable sets 12
Chapter 2. P. Jones traveling salesman theorem 17
1. The /3 numbers 17
2. Characterization of subsets of rectifiable curves 20
3. Uniformly rectifiable sets 23
Chapter 3. Menger curvature 29
1. Definition and basic properties 29
2. Menger curvature and Lipschitz graphs 31
3. Menger curvature and /3 numbers 32
4. Menger curvature and Cantor type sets 44
5. P. Jones construction of good measures supported on continua 46
Chapter 4. The Cauchy singular integral operator on Ahlfors regular sets 55
1. The Hilbert transform 55
2. Singular integral operators 56
3. The Hardy Littlewood maximal operator 58
4. The Calderon Zygmund theory 59
5. The Tl and the Tb theorems 59
6. I2 boundedness of the Cauchy singular operator on Lipschitz graphs 61
7. Cauchy singular operator and rectifiability 63
Chapter 5. Analytic capacity and the Painleve problem 67
1. Removable singularities 67
2. The Painleve Problem 68
3. Some examples 70
4. Analytic capacity and metric size of sets 74
5. Garnett Ivanov s counterexample 75
6. Who was Painleve ? 78
Chapter 6. The Denjoy and Vitushkin conjectures 81
1. The statements 81
2. The standard duality argument 82
3. Proof of the Denjoy conjecture 84
xii CONTENTS
4. Proof of the Vitushkin conjecture 90
5. The Vitushkin conjecture for sets with infinite length 100
Chapter 7. The capacity 7+ and the Painleve Problem 105
1. Melnikov s inequality 105
2. Tolsa s solution of the Painleve problem 108
3. Concluding remarks and open problems 112
Bibliography 115
Index 119
|
| any_adam_object | 1 |
| author | Pajot, Hervé |
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| dewey-raw | 514.42 |
| dewey-search | 514.42 |
| dewey-sort | 3514.42 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T19:07:28Z |
| institution | BVB |
| isbn | 3540000011 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010022246 |
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| physical | XII, 118 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
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| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Pajot, Hervé Verfasser aut Analytic capacity, rectifiability, menger curvature and the cauchy integral Hervé Pajot Berlin ; Heidelberg ; New York ; Hong Kong ; London ; Milan ; Pa Springer 2002 XII, 118 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1799 Geometrische Maßtheorie - Analytische Kapazität - Cauchy-Integral Geometrische Maßtheorie (DE-588)4125258-5 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Cauchy-Integral (DE-588)4511419-5 gnd rswk-swf Analytische Kapazität (DE-588)4200459-7 gnd rswk-swf Kapazität Mathematik (DE-588)4163239-4 gnd rswk-swf Geometrische Maßtheorie (DE-588)4125258-5 s DE-604 Harmonische Analyse (DE-588)4023453-8 s Kapazität Mathematik (DE-588)4163239-4 s Analytische Kapazität (DE-588)4200459-7 s Cauchy-Integral (DE-588)4511419-5 s Lecture notes in mathematics 1799 (DE-604)BV000676446 1799 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010022246&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pajot, Hervé Analytic capacity, rectifiability, menger curvature and the cauchy integral Lecture notes in mathematics Geometrische Maßtheorie - Analytische Kapazität - Cauchy-Integral Geometrische Maßtheorie (DE-588)4125258-5 gnd Harmonische Analyse (DE-588)4023453-8 gnd Cauchy-Integral (DE-588)4511419-5 gnd Analytische Kapazität (DE-588)4200459-7 gnd Kapazität Mathematik (DE-588)4163239-4 gnd |
| subject_GND | (DE-588)4125258-5 (DE-588)4023453-8 (DE-588)4511419-5 (DE-588)4200459-7 (DE-588)4163239-4 |
| title | Analytic capacity, rectifiability, menger curvature and the cauchy integral |
| title_auth | Analytic capacity, rectifiability, menger curvature and the cauchy integral |
| title_exact_search | Analytic capacity, rectifiability, menger curvature and the cauchy integral |
| title_full | Analytic capacity, rectifiability, menger curvature and the cauchy integral Hervé Pajot |
| title_fullStr | Analytic capacity, rectifiability, menger curvature and the cauchy integral Hervé Pajot |
| title_full_unstemmed | Analytic capacity, rectifiability, menger curvature and the cauchy integral Hervé Pajot |
| title_short | Analytic capacity, rectifiability, menger curvature and the cauchy integral |
| title_sort | analytic capacity rectifiability menger curvature and the cauchy integral |
| topic | Geometrische Maßtheorie - Analytische Kapazität - Cauchy-Integral Geometrische Maßtheorie (DE-588)4125258-5 gnd Harmonische Analyse (DE-588)4023453-8 gnd Cauchy-Integral (DE-588)4511419-5 gnd Analytische Kapazität (DE-588)4200459-7 gnd Kapazität Mathematik (DE-588)4163239-4 gnd |
| topic_facet | Geometrische Maßtheorie - Analytische Kapazität - Cauchy-Integral Geometrische Maßtheorie Harmonische Analyse Cauchy-Integral Analytische Kapazität Kapazität Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010022246&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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