Isomorphisms between H1 Spaces / by Paul F.X. Müller
(Monografie Matematyczne, Instytut Matematyczny Polskiej Akademii Nauk (IMPAN) ; 66)
| データ種別 | 電子ブック |
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| 出版情報 | Basel : Birkhäuser Basel , 2005 |
| 本文言語 | 英語 |
| 大きさ | XIV, 458 p : online resource |
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| 内容注記 | The Haar System: Basic Facts and Classical Results Projections, Isomorphisms and Interpolation Combinatorics of Colored Dyadic Intervals Martingale H1 Spaces Isomorphic Invariants for H1 Atomic H1 Spaces |
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| 一般注記 | This book presents a thorough and self-contained presentation of H¹ and its known isomorphic invariants, such as the uniform approximation property, the dimension conjecture, and dichotomies for the complemented subspaces. The necessary background is developed from scratch. This includes a detailed discussion of the Haar system, together with the operators that can be built from it (averaging projections, rearrangement operators, paraproducts, Calderon-Zygmund singular integrals). Complete proofs are given for the classical martingale inequalities of C. Fefferman, Burkholder, and Khinchine-Kahane, and for large deviation inequalities. Complex interpolation, analytic families of operators, and the Calderon product of Banach lattices are treated in the context of H^p spaces. Througout the book, special attention is given to the combinatorial methods developed in the field, particularly J. Bourgain's proof of the dimension conjecture, L. Carleson's biorthogonal system in H¹, T. Figiel's integral representation, W.B. Johnson's factorization of operators, B. Maurey's isomorphism, and P. Jones' proof of the uniform approximation property. An entire chapter is devoted to the study of combinatorics of colored dyadic intervals |
| 著者標目 | *Müller, Paul F.X. author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Mathematical analysis LCSH:Analysis (Mathematics) LCSH:Harmonic analysis LCSH:Functional analysis LCSH:Probabilities FREE:Mathematics FREE:Analysis FREE:Abstract Harmonic Analysis FREE:Functional Analysis FREE:Probability Theory and Stochastic Processes |
| 分 類 | DC23:515 |
| 巻冊次 | ISBN:9783764373450 
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| ISBN | 9783764373450 |
| URL | http://dx.doi.org/10.1007/b137684 |
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