Operator Valued Hardy Spaces

by Mei, Tao

• ISBN13: 9780821839805
• ISBN10: 0821839802
• Format: Paperback
• Copyright: 2007-07-22
• Publisher: Amer Mathematical Society

Summary

The author gives a systematic study of the Hardy spaces of functions with values in the noncommutative $Lp$-spaces associated with a semifinite von Neumann algebra $\mathcal{M .$ This is motivated by matrix valued Harmonic Analysis (operator weighted norm inequalities, operator Hilbert transform), as well as by the recent development of noncommutative martingale inequalities. in this paper noncommutative Hardy spaces are defined by noncommutative Lusin integral function, and it isproved that they are equivalent to those defined by noncommutative Littlewood-Paley G-functions. The main results of this paper include: (i) The analogue in the author's setting of the classical Fefferman duality theorem between $\mathcal{H 1$ and $\mathrm{BMO $. (ii) The atomic decomposition of theauthor's noncommutative $\mathcal{H 1.$ (iii) The equivalence between the norms of the noncommutative Hardy spaces and of the noncommutative $Lp$-spaces $(1

Table of Contents

Introduction

Preliminaries

The Duality between $\mathcal H^1$ and BMO

The maximal inequality

The duality between $\mathcal H^p$ and $\textrm{BMO}^q, 1 < p < 2$

Reduction of BMO to dyadic

BMO Interpolation

Bibliography

Table of Contents provided by Publisher. All Rights Reserved.

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