Harmonic measure:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY [u.a.]
Cambridge Univ. Press
2008
|
| Ausgabe: | Paperback ed. 1. publ. |
| Schriftenreihe: | New mathematical monographs
2 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and indexes |
| Beschreibung: | XV, 571 S. Ill., graph. Darst. |
| ISBN: | 0521720605 9780521720601 9780521470186 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV036061388 | ||
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| 007 | t | ||
| 008 | 100303s2008 xxuad|| |||| 00||| eng d | ||
| 020 | |a 0521720605 |9 0-521-72060-5 | ||
| 020 | |a 9780521720601 |9 978-0-521-72060-1 | ||
| 020 | |a 9780521470186 |9 978-0-521-47018-6 | ||
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| 084 | |a SK 450 |0 (DE-625)143240: |2 rvk | ||
| 084 | |a MAT 310f |2 stub | ||
| 100 | 1 | |a Garnett, John B. |d 1940- |e Verfasser |0 (DE-588)13370856X |4 aut | |
| 245 | 1 | 0 | |a Harmonic measure |c John B. Garnett ; Donald E. Marshall |
| 250 | |a Paperback ed. 1. publ. | ||
| 264 | 1 | |a New York, NY [u.a.] |b Cambridge Univ. Press |c 2008 | |
| 300 | |a XV, 571 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a New mathematical monographs |v 2 | |
| 500 | |a Includes bibliographical references and indexes | ||
| 650 | 4 | |a aFunctions of complex variables | |
| 650 | 4 | |a aPotential theory (Mathematics) | |
| 650 | 0 | 7 | |a Maßtheorie |0 (DE-588)4074626-4 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Maßtheorie |0 (DE-588)4074626-4 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Marshall, Donald E. |d 1947- |e Verfasser |0 (DE-588)135730929 |4 aut | |
| 830 | 0 | |a New mathematical monographs |v 2 |w (DE-604)BV035420183 |9 2 | |
| 856 | 4 | 2 | |m Digitalisierung UB Passau |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018952861&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-018952861 | ||
Datensatz im Suchindex
| _version_ | 1804141105864769536 |
|---|---|
| adam_text | Contents
Preface
page
xiii
I. Jordan Domains
1
1.
The Half-Plane and the Disc
1
2.
Fatou s Theorem and Maximal Functions
6
3.
Carathéodory s
Theorem
13
4.
Distortion and the Hyperbolic Metric
16
5.
The Hayman-Wu Theorem
23
Notes
25
Exercises and Further Results
26
II. Finitely Connected Domains
1.
The
Schwarz
Alternating Method
2.
Green s Functions and
Poisson
Kernels
3.
Conjugate Functions
4.
Boundary Smoothness
Notes
Exercises and Further Results
III. Potential Theory
1.
Capacity and Green s Functions
2.
The Logarithmic Potential
3.
The Energy Integral
4.
The Equilibrium Distribution
5.
Wiener s Solution to the Dirichlet Problem
6.
Regular Points
7.
Wiener Series
8.
Polar Sets and Sets of Harmonic Measure Zero
9.
Estimates for Harmonic Measure
104
Notes
112
Exercises and Further Results
112
IV. Extremal Distance
129
1.
Definitions and Examples
129
2.
Uniqueness of Extremal Metrics
133
3.
Four Rules for Extremal Length
134
4.
Extremal Metrics for Extremal Distance
139
5.
Extremal Distance and Harmonic Measure
143
6.
The
ƒ
^y Estimate
146
Notes
149
Exercises and Further Results
150
V. Applications and Reverse Inequalities
157
1.
Asymptotic Values of Entire Functions
157
2.
Lower Bounds
159
3.
Reduced Extremal Distance
162
4. Teichmüller
s
Modulsatz 166
5.
Boundary Conformality and Angular Derivatives
173
6.
Conditions More Geometric
184
Notes
193
Exercises and Further Results
194
VI. Simply Connected Domains, Part One
200
1.
The F. and M. Riesz Theorem
200
2.
Privalov s Theorem and Plessner s Theorem
203
3.
Accessible Points
205
4.
Cone Points and McMillan s Theorem
207
5.
Compression and Expansion
212
6.
Pommerenke s Extension
216
Notes
221
Exercises and Further Results
221
VII. Bloch
Functions and Quasicircles
229
1.
Bloch Functions
229
2.
Bloch Functions and
Univalent
Functions
232
3.
Quasicircles
241
4.
Chord-Arc Curves and the A°° Condition
246
5.
BMO Domains
253
Notes
257
Exercises and Further Results
258
VIII.
Simply Connected
Domains,
Part Two
269
1.
The Law of the Iterated Logarithm for
В
loch Functions
269
2.
Harmonic Measure and Hausdorff Measure
272
3.
The Number of Bad Discs
281
4.
Brennan s Conjecture and Integral Means Spectra
286
5.
β
Numbers and Polygonal Trees
289
6.
The Dandelion Construction and (c)
=>■
(a)
296
7.
Baernstein s Example on the Hayman-Wu Theorem
302
Notes
305
Exercises and Further Results
307
IX. Infinitely Connected Domains
315
1.
Cantor Sets
315
2.
For Certain
Ω,
dim
ω
< 1. 324
3.
For All
Ω,
dim
ω
< 1. 331
Notes
341
Exercises and Further Results
342
X. Rectifiability and Quadratic Expressions
347
1.
The Lusin Area Function
348
2.
Square Sums and Rectifiability
361
3.
A Decomposition Theorem
372
4.
Schwarzian Derivatives
380
5.
Geometric Estimates of Schwarzian Derivatives
384
6.
Schwarzian Derivatives and Rectifiable Quasicircles
393
7.
The Bishop-Jones
т~ц
Theorem
397
8.
Schwarzian Derivatives and
В
MO Domains
410
9.
Angular Derivatives
412
10.
A Local F. and M. Riesz Theorem
416
11.
Ahlfors Regular Sets and the Hayman-Wu Theorem
421
Notes
426
Exercises and Further Results
427
Appendices
435
A. Hardy Spaces
435
B. Mixed Boundary Value Problems
441
С
The Dirichlet Principle
447
D. Hausdorff Measure
456
E. Transfinite
Diameter and Evans Functions
466
F. Martingales, Brownian Motion, and Kakutani s Theorem
470
G. Carleman s Method
480
H.
Extremal
Distance
in Finitely Connected Domains
484
I. McMillan s Twist Point Theorem
497
J. Bloch Martingales and the Law of the Iterated Logarithm
503
K. A Dichotomy Theorem
512
L. Two Estimates on Integral Means
518
M.
Calderón s
Theorem and Chord-Arc Domains
520
Bibliography
531
Author Index
555
Symbol Index
559
Subject Index
561
|
| any_adam_object | 1 |
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| discipline | Mathematik |
| edition | Paperback ed. 1. publ. |
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| id | DE-604.BV036061388 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:10:35Z |
| institution | BVB |
| isbn | 0521720605 9780521720601 9780521470186 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018952861 |
| oclc_num | 633899699 |
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| owner | DE-739 DE-706 DE-824 DE-11 |
| owner_facet | DE-739 DE-706 DE-824 DE-11 |
| physical | XV, 571 S. Ill., graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | New mathematical monographs |
| series2 | New mathematical monographs |
| spelling | Garnett, John B. 1940- Verfasser (DE-588)13370856X aut Harmonic measure John B. Garnett ; Donald E. Marshall Paperback ed. 1. publ. New York, NY [u.a.] Cambridge Univ. Press 2008 XV, 571 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier New mathematical monographs 2 Includes bibliographical references and indexes aFunctions of complex variables aPotential theory (Mathematics) Maßtheorie (DE-588)4074626-4 gnd rswk-swf Maßtheorie (DE-588)4074626-4 s DE-604 Marshall, Donald E. 1947- Verfasser (DE-588)135730929 aut New mathematical monographs 2 (DE-604)BV035420183 2 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018952861&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Garnett, John B. 1940- Marshall, Donald E. 1947- Harmonic measure New mathematical monographs aFunctions of complex variables aPotential theory (Mathematics) Maßtheorie (DE-588)4074626-4 gnd |
| subject_GND | (DE-588)4074626-4 |
| title | Harmonic measure |
| title_auth | Harmonic measure |
| title_exact_search | Harmonic measure |
| title_full | Harmonic measure John B. Garnett ; Donald E. Marshall |
| title_fullStr | Harmonic measure John B. Garnett ; Donald E. Marshall |
| title_full_unstemmed | Harmonic measure John B. Garnett ; Donald E. Marshall |
| title_short | Harmonic measure |
| title_sort | harmonic measure |
| topic | aFunctions of complex variables aPotential theory (Mathematics) Maßtheorie (DE-588)4074626-4 gnd |
| topic_facet | aFunctions of complex variables aPotential theory (Mathematics) Maßtheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018952861&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV035420183 |
| work_keys_str_mv | AT garnettjohnb harmonicmeasure AT marshalldonalde harmonicmeasure |