E Book

Isomorphisms Between H¹ Spaces

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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.

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Ketersediaan

Informasi Detail

Judul Seri

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No. Panggil

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Penerbit

Basel : Birkhauser., 2005

Deskripsi Fisik

XIV, 458 p.online resource.

Bahasa

English

ISBN/ISSN

9783764373450

Klasifikasi

515

Tipe Isi

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Tipe Media

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Tipe Pembawa

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Edisi

1st ed. 2005.

Subjek

Probabilities.
Probability Theory and Stochastic Processes.
Mathematical analysis.
Analysis (Mathematics).
Analysis.
Harmonic analysis.
Abstract Harmonic Analysis.
Functional analysis.

Info Detail Spesifik

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Pernyataan Tanggungjawab

Paul F.X. Müller.

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