Analysis of and on uniformly rectifiable sets:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[1993]
|
| Schriftenreihe: | Mathematical surveys and monographs
Volume 38 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006185816&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | xii, 356 Seiten Illustrationen, Diagramme |
| ISBN: | 0821815377 9780821815373 |
Internformat
MARC
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| 245 | 1 | 0 | |a Analysis of and on uniformly rectifiable sets |c Guy David ; Stephen Semmes |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [1993] | |
| 264 | 4 | |c © 1993 | |
| 300 | |a xii, 356 Seiten |b Illustrationen, Diagramme | ||
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Datensatz im Suchindex
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|---|---|
| adam_text | Table of Contents
Preface ix
Notation and Conventions xi
PART I: Background Information and the Statements of the
Main Results
Chapter 1. Reviews of Various Topics 3
1.1 Review from geometric measure theory 3
1.2 Review of some topics concerning singular integral operators
and rectifiability 7
1.3 Review of some aspects of Littlewood Paley theory in
connection with rectifiability 16
1.4 Various characterizations of uniform rectifiability 21
1.5 The weak geometric lemma and its relatives 26
Chapter 2. A Summary of the Main Results 31
2.1 The results of Part II 31
2.2 Bilateral approximation from a functorial point of view 37
2.3 The results of Part III 42
2.4 A rapid description of Part IV 50
Chapter 3. Dyadic Cubes and Corona Decompositions 53
3.1 Cubes 53
3.2 Corona decompositions 55
3.3 Generalized corona decompositions 63
PART II: New Geometrical Conditions Related to Uniform
Rectifiability
Chapter 1. One Dimensional Sets 69
1.1 The weak connectedness condition 69
1.2 The weaker local symmetry condition (d 1) 77
1.3 Weak constant density for one dimensional sets 86
1.4 The weak two points on spheres condition 93
V
vi TABLE OF CONTENTS
Chapter 2. The Bilateral Weak Geometric Lemma and its Variants 97
2.1 Introduction; the corona method 97
2.2 Big projections in codimension 1 104
2.3 Big projections in the higher codimension case 110
2.4 The local convexity condition LCV 120
2.5 The weaker local convexity condition WLCV 126
2.6 Weak starlikeness 129
2.7 Some questions about variants of the LCV and the LS 131
Chapter 3. The WHIP and Related Conditions 135
3.1 The WHIP, the WTP, and uniform rectifiability 135
3.2 The WHIP and weaker versions of the BWGL 138
3.3 The weak exterior convexity condition and the GWEC 141
3.4 The weak no mugs, weak no boxes, and weak no reels
conditions 147
3.5 The proof of Theorem 3.9 (part 1) 154
3.6 Part 2 of the proof: The stopping time argument 165
Chapter 4. Other Conditions in the Codimension 1 Case 183
4.1 Introduction 183
4.2 Labellings 187
4.3 The derivation of Theorem 4.9 from Theorem 4.31 196
PART III: Applications
Chapter 1. Uniform Rectifiability and Singular Integral Operators 207
1.1 Preliminaries 207
1.2 Step one 208
1.3 Step two 212
1.4 An abstraction of § 3 214
Chapter 2. Uniform Rectifiability and Square Function Estimates for
the Cauchy Kernel 217
2.1 Some general comments about square function estimates 217
2.2 Uniform rectifiability implies the USFE when d = 1 219
2.3 From square function estimates to uniform rectifiability:
Preliminary reductions and the plan of the proof 226
2.4 The proof of Lemma 2.36 229
2.5 A topological lemma 232
2.6 The main step in the proof of Proposition 2.38 234
2.7 The end of the proof of Proposition 2.38 244
Chapter 3. Square Function Estimates and Uniform Rectifiability in
Higher Dimensions 249
3.1 A brief review of Clifford analysis 249
3.2 Clifford analysis and square function estimates 251
TABLE OF CONTENTS vii
3.3 From square functions to uniform rectifiability: Preliminary
reductions 252
3.4 Cauchy flatness implies rectifiability 253
3.5 The analogue of Proposition 2.59 256
3.6 Cauchy flatness implies weak flatness 261
3.7 Weak flatness implies exterior convexity 265
3.8 Some remarks about the higher codimension case 267
Chapter 4. Approximating Lipschitz Functions by Affine Functions 269
4.1 The direct estimates 269
4.2 The converse when d = 1 279
4.3 A more abstract version of the WALA 293
Chapter 5. The Weak Constant Density Condition 297
5.1 Compactness will only get you so far 297
5.2 The codimension 1 case, part 1 301
5.3 A general lemma about Carleson packing conditions 305
5.4 The codimension 1 case, part 2 306
5.5 The weak dyadic density condition 307
PART IV: Direct Arguments for Some Stability Results
Chapter 1. Stability of Various Versions of the Geometric Lemma 313
1.1 The statements 313
1.2 A John Nirenberg Stromberg lemma for Carleson packing
conditions 315
1.3 Two lemmas on approximations of regular sets by af planes 318
1.4 The proof of the theorems 324
Chapter 2. Stability Properties of the Corona Decomposition 327
2.1 Corona decompositions revisited 327
2.2 Corona constructions and Lipschitz functions 328
2.3 The statement of the main result 336
2.4 Preliminaries 336
2.5 The proof of Lemma 2.38 340
References 345
Table of Selected Notation 349
Table of Acronyms 351
Table of Theorems 353
Index 355
|
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| id | DE-604.BV009295687 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T09:35:42Z |
| institution | BVB |
| isbn | 0821815377 9780821815373 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006185816 |
| oclc_num | 246872914 |
| open_access_boolean | |
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| owner_facet | DE-12 DE-739 DE-29T DE-355 DE-BY-UBR DE-11 DE-188 |
| physical | xii, 356 Seiten Illustrationen, Diagramme |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spellingShingle | David, Guy 1957- Semmes, Stephen 1962- Analysis of and on uniformly rectifiable sets Mathematical surveys and monographs Geometrische Maßtheorie - Singulärer Integraloperator Singuläres Integral (DE-588)4181533-6 gnd Hausdorff-Maß (DE-588)4159238-4 gnd |
| subject_GND | (DE-588)4181533-6 (DE-588)4159238-4 |
| title | Analysis of and on uniformly rectifiable sets |
| title_auth | Analysis of and on uniformly rectifiable sets |
| title_exact_search | Analysis of and on uniformly rectifiable sets |
| title_full | Analysis of and on uniformly rectifiable sets Guy David ; Stephen Semmes |
| title_fullStr | Analysis of and on uniformly rectifiable sets Guy David ; Stephen Semmes |
| title_full_unstemmed | Analysis of and on uniformly rectifiable sets Guy David ; Stephen Semmes |
| title_short | Analysis of and on uniformly rectifiable sets |
| title_sort | analysis of and on uniformly rectifiable sets |
| topic | Geometrische Maßtheorie - Singulärer Integraloperator Singuläres Integral (DE-588)4181533-6 gnd Hausdorff-Maß (DE-588)4159238-4 gnd |
| topic_facet | Geometrische Maßtheorie - Singulärer Integraloperator Singuläres Integral Hausdorff-Maß |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006185816&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000018014 |
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