Martingales in Banach spaces:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2016
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| Series: | Cambridge studies in advanced mathematics
155 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Item Description: | Literaturverzeichnis: Seite 542-559 |
| Physical Description: | xxviii, 561 Seiten Diagramme |
| ISBN: | 9781107137240 1107137241 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804176495953838080 |
|---|---|
| adam_text | Contents Introduction Description of the contents page x xiv 1 Banach space valued martingales 1.1 Banach space valued ¿^-spaces 1.2 Banach space valued conditional expectation 1.3 Martingales: basic properties 1.4 Examples of filtrations 1.5 Stopping times 1.6 Almost sure convergence: Maximal inequalities 1.7 Independent increments 1.8 Phillips’s theorem 1.9 Reverse martingales 1.10 Continuous time* 1.11 Notes and remarks 1 1 7 9 12 17 19 28 31 34 36 41 2 Radon-Nikodým property 2.1 Vector measures 2.2 Martingales, dentability and the Radon-Nikodým 42 42 2.3 2.4 2.5 2.6 2.7 2.8 property The dual of LP(B) Generalizations of LpfB) The Krein-Milman property Edgar’s Choquet theorem The Lewis-Stegall theorem Notes and remarks 46 57 60 63 67 70 73 v
vi Contents 76 76 80 Harmonic functions and RNP 3.1 Harmonicity and the Poisson kernel 3.2 The hp spaces of harmonic functions on D 3.3 Non-tangential maximal inequalities: boundary behaviour 3.4 Harmonic functions and RNP 3.5 Brownian martingales* 3.6 Notes and remarks 87 97 101 110 Analytic functions and ARNP 4.1 Subharmonic functions 4.2 Outer functions and HP(D) 4.3 Banach space valued Hp-spaces for 0 p oo 4.4 Analytic Radon-Nikodým property 4.5 Hardy martingales and Brownian motion* 4.6 Ջ֊ valued hp and Hp over the half-plane U* 4.7 Further complements* 4.8 Notes and remarks 112 112 116 118 127 131 140 146 148 The UMD property for Banach spaces 5.1 Martingale transforms (scalar case): Burkholder’s inequalities 5.2 Square functions for В-valued martingales: Kahane’s inequalities 5.3 Definition of UMD 5.4 Gundy’s decomposition 5.5 Extrapolation 5.6 The UMDi property: Burgess Davis decomposition 5.7 Examples: UMD implies super-RNP 5.8 Dyadic UMD implies UMD 5.9 The Burkholder-Rosenthal inequality 5.10 Stein inequalities in UMD spaces 5.11 Burkholder’s geometric characterization of UMD space 5.12 Appendix: hypercontractivity on {—1, 1} 5.13 Appendix: Hölder-Minkowski inequality 5.14 Appendix: basic facts on weak-Lp 5.15 Appendix: reverse Hôlder principle 5.16 Appendix: Marcinkiewicz theorem 5.17 Appendix: exponential inequalities and growth of Lp- norms 5.18 Notes and remarks 151 151 154 159 162 168 175 180 183 190 195 197 206 207 209 210 212 214 214
vii Contents 6 7 The Hilbert transform and UMD Banach spaces 6.1 Hilbert transform: HT spaces 6.2 Bourgain’s transference theorem: HT implies UMD 6.3 UMD implies HT 6.4 UMD implies HT (with stochastic integrals)* 6.5 Littlewood-Paley inequalities in UMD spaces 6.6 The Walsh system Hilbert transform 6.7 Analytic UMD property* 6.8 UMD operators* 6.9 Notes and remarks Banach space valued Я1 and BMO 7.1 Banach space valued H1 and BMO: Fefferman’s duality theorem 7.2 Atomic Ք-valued H1 7.3 H1, BMO and atoms for martingales 7.4 Regular filtrations 7.5 From dyadic BMO to classical BMO 7.6 Notes and remarks 218 218 228 233 246 249 254 255 257 260 263 263 266 282 291 292 297 8 Interpolation methods (complex and real) 8.1 The unit strip 8.2 The complex interpolation method 8.3 Duality for the complex method 8.4 The real interpolation method 8.5 Real interpolation between ¿^-spaces 8.6 The ^-functional for (Li (Bo), L^Bi )) 8.7 Real interpolation between vector valued Lp-spaces 8.8 Duality for the real method 8.9 Reiteration for the real method 8.10 Comparing the real and complex methods 8.11 Symmetric and self-dual interpolation pairs 8.12 Notes and remarks 299 300 303 321 332 336 342 346 352 357 362 363 368 9 The strong p-variation of scalar valued martingales 9.1 Notes and remarks 372 380 10 Uniformly convex Banach space valued martingales 10.1 Uniform convexity 10.2 Uniform smoothness 10.3 Uniform convexity and smoothness of Lp 10.4 Type, cotype and UMD 382 382 395 404 406
Contents viii 10.5 10.6 10.7 Square function inequalities in ^-uniformly convex and p-uniformly smooth spaces Strong p-variation, uniform convexity and smoothness Notes and remarks 417 423 425 11 Super-reflexivity 11.1 Finite representability and super-properties 11.2 Super-reflexivity and inequalities for basic sequences 11.3 Uniformly non-square and J-convex spaces 11.4 Super-reflexivity and uniform convexity 11.5 Strong law of large numbers and super-reflexivity 11.6 Complex interpolation: Ժ-Hilbertian spaces 11.7 Complex analogues of uniform convexity* 11.8 Appendix: ultrafilters, ultraproducts 11.9 Notes and remarks 428 428 433 446 454 457 459 463 472 474 12 Interpolation between strong p-variation spaces 12.1 The spaces vp(B), Wp(B) and WP4(B) 12.2 Duality and quasi-reflexivity 12.3 The intermediate spaces up(B) and vp(B) 12.4 ¿^-spaces with values in vp and Wp 12.5 Some applications 12.6 А-functional for (vr(B )y t^B)) 12.7 Strong p-variation in approximation theory 12.8 Notes and remarks 477 478 482 485 489 492 494 496 499 13 Martingales and metric spaces 13.1 Exponential inequalities 13.2 Concentration of measure 13.3 Metric characterization of super-reflexivity: trees 13.4 Another metric characterization of super-reflexivity: diamonds 13.5 Markov type p and uniform smoothness 13.6 Notes and remarks 500 500 503 506 14 An invitation to martingales in non-commutative ¿^-spaces* 14.1 Non-commutative probability space 14.2 Non-commutative ¿^-spaces 14.3 Conditional expectations: non-commutative martingales 14.4 Examples 512 519 521 523 523 524 527 529
Contents 14.5 14.6 14.7 14.8 14.9 14.10 Non-commutative Khintchin inequalities Non-commutative Burkholder inequalities Non-commutative martingale transforms Non-commutative maximal inequalities Martingales in operator spaces Notes and remarks Bibliography Index ix 531 533 535 537 539 541 542 560
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| any_adam_object | 1 |
| author | Pisier, Gilles 1950- |
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| dewey-full | 519.2/87 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2/87 |
| dewey-search | 519.2/87 |
| dewey-sort | 3519.2 287 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV043708735 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:33:06Z |
| institution | BVB |
| isbn | 9781107137240 1107137241 |
| language | English |
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| physical | xxviii, 561 Seiten Diagramme |
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| publishDate | 2016 |
| publishDateSearch | 2016 |
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| publisher | Cambridge University Press |
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| series | Cambridge studies in advanced mathematics |
| series2 | Cambridge studies in advanced mathematics |
| spelling | Pisier, Gilles 1950- Verfasser (DE-588)113782268 aut Martingales in Banach spaces Gilles Pisier, Texas A&M University Cambridge Cambridge University Press 2016 xxviii, 561 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Cambridge studies in advanced mathematics 155 Literaturverzeichnis: Seite 542-559 Martingales (Mathematics) Banach-Raum (DE-588)4004402-6 gnd rswk-swf Martingal (DE-588)4126466-6 gnd rswk-swf Banach-Raum (DE-588)4004402-6 s Martingal (DE-588)4126466-6 s DE-604 Erscheint auch als Online-Ausgabe Pisier, Gilles Martingales in Banach spaces 978-1-316-48058-8 Cambridge studies in advanced mathematics 155 (DE-604)BV000003678 155 DE-601 pdf/application http://www.gbv.de/dms/bowker/toc/9781107137240.pdf Inhaltsverzeichnis Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029120995&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pisier, Gilles 1950- Martingales in Banach spaces Cambridge studies in advanced mathematics Martingales (Mathematics) Banach-Raum (DE-588)4004402-6 gnd Martingal (DE-588)4126466-6 gnd |
| subject_GND | (DE-588)4004402-6 (DE-588)4126466-6 |
| title | Martingales in Banach spaces |
| title_auth | Martingales in Banach spaces |
| title_exact_search | Martingales in Banach spaces |
| title_full | Martingales in Banach spaces Gilles Pisier, Texas A&M University |
| title_fullStr | Martingales in Banach spaces Gilles Pisier, Texas A&M University |
| title_full_unstemmed | Martingales in Banach spaces Gilles Pisier, Texas A&M University |
| title_short | Martingales in Banach spaces |
| title_sort | martingales in banach spaces |
| topic | Martingales (Mathematics) Banach-Raum (DE-588)4004402-6 gnd Martingal (DE-588)4126466-6 gnd |
| topic_facet | Martingales (Mathematics) Banach-Raum Martingal |
| url | http://www.gbv.de/dms/bowker/toc/9781107137240.pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029120995&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003678 |
| work_keys_str_mv | AT pisiergilles martingalesinbanachspaces |
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