Isomorphisms Between H¹ Spaces

ISBN-13: 9783764324315 / Angielski / Twarda / 2005 / 458 str.

Paul F. X. Muller; Paul F. X. M]ller; P. V. X. Muller

Opis

This book gives a thorough and self contained presentation of H, its known isomorphic invariants and a complete classification of H on spaces of homogeneous type. 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. Complete proofs are given for the classical martingale inequalities, and for large deviation inequalities. Complex interpolation is treated. Througout, special attention is given to the combinatorial methods developed in the field. An entire chapter is devoted to study the combinatorics of coloured dyadic Intervals."

Recenzje

"Ein bedeutendes, in Inhalt und Form vorzügliches Standardwerk über faszinierende, tiefliegende mathematische Probleme vor, zu deren Lösung viele der besten Mathematiker beigetragen haben." (Monatshefte für Mathematik)

Spis treści

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.

Blurb

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.