Martingale spaces and inequalities:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Beijing
Peking Univ. Press [u.a.]
1993
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IV, 344 S. |
| ISBN: | 7301020694 3528083972 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
1 Probabilistic Preliminaries 1
1.1 Conditional expectations 1
1.2 Stopping times 6
1.3 Martingales, super (or sub )martingales 10
1.3.1 Decompositions of martingales, super (or sub )martingales 13
1.3.2 Convergences of martingales, super (or sub )martingales 21
2 HP(p 1) Martingales 33
2.1 Boundedness of M and S, equivalence between M and S 33
2.2 Dual spaces of Hp, Fefferman s inequality 42
2.3 Prom Fefferman s inequality to Davis inequality 47
2.4 Davis decomposition for Hp, the Spaces Tp and Ap 51
2.5 Another proof of Fefferman s theorem (via Davis decomposition
and atomic decomposition) 53
2.6 Weak compactness and convergence in Hi 61
2.7 The spaces /ip(0 p oo) 65
2.8 Dual spaces of hp and Vp 69
3 ^ inequalities on Martingales 81
3.1 Convex functions with moderate growth 81
3.2 Convex ^ inequalities 85
3.3 Convex ^ inequalities with 3$ 1 94
3.4 Concave ^ inequalities 104
3..5 General ^ inequalities 109
3.6 Rearrangement inequalities 117
4 BMO Martingales 129
4.1 John Nirenberg s theorem 130
4.2 Other characterizations of BMO 134
4.3 BMO and BLO 141
4.4 Carleson measures and BMO 154
4.5 Commutator theory related to BMO 156
4.6 Distance of / £ BMO to L°° 163
5 Martingale Transforms 173
5.1 Martingale transforms as a technique 173
5.2 Boundedness of martingale transforms as operators 184
5.3 Paraproduct operator and some related ones 193
5.4 Some necessary conditions 203
5.5 Best constants in some martingale inequalities 207
iv Contents
6 Weight Theory and Weighted ^ inequalities 227
6.1 Ap conditions and its extensions b 227
6.2 The 6a conditions in the case A 0orA l 231
6.3 Gehring s lemma, and inverse Holder s inequality 233
6.4 Ap weights and BMO martingales 242
6.5 Factorization of Ap weights 247
6.6 Weighted ^ inequalities 248
7 Regular Martingales 263
7.1 A kind of regularity 263
7.2 Regular Hp(0 p 1) martingales 270
7.2.1 Atomic decomposition of Hp(0 p 1) 271
7.2.2 Dual spaces of Hp(0 p 1) 273
7.2.3 Interpolation theory of Hp 275
7.2.4 #i and Llog+L 284
7.2.5 Rearrangement of functions in Hp (~}ReLl(0 p 1) 285
7.2.6 Operator characterization of Hp in the g martingale case 288
7.3 Weighted ^ inequalities for regular martingales 305
8 Some Applications of Martingale Techniques
in Harmonic Analysis 313
8.1 Gundy Varopoulos backward martingales and its application
in lacunary Fourier series 314
8.2 The martingale proof of the T(b) Theorem and the related martingales 321
8.2.1 The proof of the special T(b) theorem 323
8.2.2 Martingales with respect to complex measures 326
References 337
Symbols 345
Index 346
|
| any_adam_object | 1 |
| author | Long, Ruilin |
| author_GND | (DE-588)1067944443 |
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| author_sort | Long, Ruilin |
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| bvnumber | BV008570839 |
| classification_rvk | SK 820 |
| classification_tum | MAT 464f MAT 605f |
| ctrlnum | (OCoLC)246566529 (DE-599)BVBBV008570839 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV008570839 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:21:16Z |
| institution | BVB |
| isbn | 7301020694 3528083972 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005633129 |
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| physical | IV, 344 S. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Peking Univ. Press [u.a.] |
| record_format | marc |
| spelling | Long, Ruilin Verfasser (DE-588)1067944443 aut Martingale spaces and inequalities Ruilin Long Beijing Peking Univ. Press [u.a.] 1993 IV, 344 S. txt rdacontent n rdamedia nc rdacarrier Martingal - Ungleichung Martingal (DE-588)4126466-6 gnd rswk-swf Martingal (DE-588)4126466-6 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005633129&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Long, Ruilin Martingale spaces and inequalities Martingal - Ungleichung Martingal (DE-588)4126466-6 gnd |
| subject_GND | (DE-588)4126466-6 |
| title | Martingale spaces and inequalities |
| title_auth | Martingale spaces and inequalities |
| title_exact_search | Martingale spaces and inequalities |
| title_full | Martingale spaces and inequalities Ruilin Long |
| title_fullStr | Martingale spaces and inequalities Ruilin Long |
| title_full_unstemmed | Martingale spaces and inequalities Ruilin Long |
| title_short | Martingale spaces and inequalities |
| title_sort | martingale spaces and inequalities |
| topic | Martingal - Ungleichung Martingal (DE-588)4126466-6 gnd |
| topic_facet | Martingal - Ungleichung Martingal |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005633129&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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