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Isomorphisms Between H¹ Spaces / by Paul F.X. Müller
(Monografie Matematyczne. ISSN:22970274 ; 66)
版 | 1st ed. 2005. |
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出版者 | (Basel : Birkhäuser Basel : Imprint: Birkhäuser) |
出版年 | 2005 |
本文言語 | 英語 |
大きさ | XIV, 458 p : online resource |
著者標目 | *Müller, Paul F.X author SpringerLink (Online service) |
件 名 | LCSH:Mathematical analysis LCSH:Harmonic analysis LCSH:Functional analysis LCSH:Probabilities FREE:Analysis FREE:Abstract Harmonic Analysis FREE:Functional Analysis FREE:Probability Theory |
一般注記 | 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 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 HTTP:URL=https://doi.org/10.1007/b137684 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9783764373450 |
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電子リソース |
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EB00232299 |
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データ種別 | 電子ブック |
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分 類 | LCC:QA299.6-433 DC23:515 |
書誌ID | 4000134413 |
ISBN | 9783764373450 |
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※2017年9月4日以降