Probabilistic behavior of harmonic functions:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel ; Boston ; Berlin
Birkhäuser Verlag
[1999]
|
| Series: | Progress in mathematics
Volume 175 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 191 - 199 |
| Physical Description: | xiv, 204 Seiten |
| ISBN: | 3764360623 0817660623 |
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MARC
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| 245 | 1 | 0 | |a Probabilistic behavior of harmonic functions |c Rodrigo Bañuelos ; Charles N. Moore |
| 264 | 1 | |a Basel ; Boston ; Berlin |b Birkhäuser Verlag |c [1999] | |
| 264 | 4 | |c © 1999 | |
| 300 | |a xiv, 204 Seiten | ||
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| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Progress in mathematics |v Volume 175 | |
| 500 | |a Literaturverz. S. 191 - 199 | ||
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| 650 | 7 | |a Fonctions harmoniques |2 ram | |
| 650 | 4 | |a Probabilités | |
| 650 | 7 | |a Probabilités |2 ram | |
| 650 | 4 | |a Harmonic functions | |
| 650 | 4 | |a Probabilities | |
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Record in the Search Index
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| adam_text | Contents
Preface vii
1 Basic Ideas and Tools 1
1.1 Harmonic functions and their basic properties 1
1.2 The Poisson kernel and Dirichlet problem for the ball 5
1.3 The Poisson kernel and Dirichlet problem for K +1 10
1.4 The Hardy Littlewood and nontangential maximal functions .... 15
1.5 Hp spaces on the upper half space 20
1.6 Some basics on singular integrals 28
1.7 The ^ function and area function 31
1.8 Classical results on boundary behavior 43
2 Decomposition into Martingales: An Invariance Principle 45
2.1 Square function estimates for sums of atoms 50
2.2 Decomposition of harmonic functions 55
2.3 Controlling errors: gradient estimates 60
3 Kolmogorov s LIL for Harmonic Functions 63
3.1 The proof of the upper half 67
3.2 The proof of the lower half 75
3.3 The sharpness of the Kolmogorov condition 81
3.4 A related LIL for the Littlewood Paley (^ function 86
4 Sharp Good A Inequalities for A and N 93
4.1 Sharp control of N by A 98
4.2 Sharp control of A by N 102
4.3 Application I. A Chung type LIL for harmonic functions 119
4.4 Application II. The Burkholder Gundy I theorem 124
xiii
xiv Contents
5 Good A Inequalities for the Density of the Area Integral 135
5.1 Sharp control of A and N by D 140
5.2 Sharp control of D by A and N 148
5.3 Application I. A Kesten type LIL and sharp Lp constants 165
5.4 Application II. The Brossard Chevalier L log L result 167
6 The Classical LIL s in Analysis 173
6.1 LIL s for lacunary series 173
6.2 LIL s for Bloch functions 178
6.3 LIL s for subclasses of the Bloch space 180
6.4 On a question of Makarov and Przytycki 185
References 191
Subject Index 200
Notation Index 203
|
| any_adam_object | 1 |
| author | Bañuelos, Rodrigo Moore, Charles Napoleon 1882-1967 |
| author_GND | (DE-588)115357151X (DE-588)1055112715 |
| author_facet | Bañuelos, Rodrigo Moore, Charles Napoleon 1882-1967 |
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| dewey-sort | 3515 253 221 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV012574597 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:29:56Z |
| institution | BVB |
| isbn | 3764360623 0817660623 |
| language | English |
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| physical | xiv, 204 Seiten |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Birkhäuser Verlag |
| record_format | marc |
| series | Progress in mathematics |
| series2 | Progress in mathematics |
| spelling | Bañuelos, Rodrigo (DE-588)115357151X aut Probabilistic behavior of harmonic functions Rodrigo Bañuelos ; Charles N. Moore Basel ; Boston ; Berlin Birkhäuser Verlag [1999] © 1999 xiv, 204 Seiten txt rdacontent n rdamedia nc rdacarrier Progress in mathematics Volume 175 Literaturverz. S. 191 - 199 Fonctions harmoniques Fonctions harmoniques ram Probabilités Probabilités ram Harmonic functions Probabilities Martingaltheorie (DE-588)4168982-3 gnd rswk-swf Harmonische Funktion (DE-588)4159122-7 gnd rswk-swf Harmonische Funktion (DE-588)4159122-7 s Martingaltheorie (DE-588)4168982-3 s DE-604 Moore, Charles Napoleon 1882-1967 (DE-588)1055112715 aut Progress in mathematics Volume 175 (DE-604)BV000004120 175 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008539896&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bañuelos, Rodrigo Moore, Charles Napoleon 1882-1967 Probabilistic behavior of harmonic functions Progress in mathematics Fonctions harmoniques Fonctions harmoniques ram Probabilités Probabilités ram Harmonic functions Probabilities Martingaltheorie (DE-588)4168982-3 gnd Harmonische Funktion (DE-588)4159122-7 gnd |
| subject_GND | (DE-588)4168982-3 (DE-588)4159122-7 |
| title | Probabilistic behavior of harmonic functions |
| title_auth | Probabilistic behavior of harmonic functions |
| title_exact_search | Probabilistic behavior of harmonic functions |
| title_full | Probabilistic behavior of harmonic functions Rodrigo Bañuelos ; Charles N. Moore |
| title_fullStr | Probabilistic behavior of harmonic functions Rodrigo Bañuelos ; Charles N. Moore |
| title_full_unstemmed | Probabilistic behavior of harmonic functions Rodrigo Bañuelos ; Charles N. Moore |
| title_short | Probabilistic behavior of harmonic functions |
| title_sort | probabilistic behavior of harmonic functions |
| topic | Fonctions harmoniques Fonctions harmoniques ram Probabilités Probabilités ram Harmonic functions Probabilities Martingaltheorie (DE-588)4168982-3 gnd Harmonische Funktion (DE-588)4159122-7 gnd |
| topic_facet | Fonctions harmoniques Probabilités Harmonic functions Probabilities Martingaltheorie Harmonische Funktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008539896&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004120 |
| work_keys_str_mv | AT banuelosrodrigo probabilisticbehaviorofharmonicfunctions AT moorecharlesnapoleon probabilisticbehaviorofharmonicfunctions |