Overview

These notes give the basic ingredients of the theory of weighted Hardy spaces of tempered distribution on Rn and illustrate the techniques used. The authors consider properties of weights in a general setting; they derive mean value inequalities for wavelet transforms and introduce halfspace techniques with, for example, nontangential maximal functions and g-functions. This leads to several equivalent definitions of the weighted Hardy space HPW. Fourier multipliers and singular integral operators are applied to the weighted Hardy spaces and complex interpolation is considered. One tool often used here is the atomic decomposition. The methods developed by the authors using the atomic decomposition in the strictly convex case p>1 are of special interest.

Full Product Details

Author:   Jan-Olov Stromberg ,  Alberto Torchinsky
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   1989 ed.
Volume:   1381
Dimensions:   Width: 17.00cm , Height: 1.00cm , Length: 24.20cm
Weight:   0.650kg
ISBN:  

9783540514022

ISBN 10:   3540514023
Pages:   200
Publication Date:   26 July 1989
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Weights.- Decomposition of weights.- Sharp maximal functions.- Functions in the upper half-space.- Extensions of distributions.- The Hardy spaces.- A dense class.- The atomic decomposition.- The basic inequality.- Duality.- Singular integrals and multipliers.- Complex interpolation.

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