Weighted Hardy Spaces

Jan-Olov Strömberg, Alberto Torchinsky (auth.)3540514023, 9783540514022, 0387514023

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.

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Table of contents :
Weights….Pages 1-17
Decomposition of weights….Pages 18-29
Sharp maximal functions….Pages 30-47
Functions in the upper half-space….Pages 48-59
Extensions of distributions….Pages 60-84
The Hardy spaces….Pages 85-102
A dense class….Pages 103-110
The atomic decomposition….Pages 111-121
The basic inequality….Pages 122-133
Duality….Pages 134-149
Singular integrals and multipliers….Pages 150-176
Complex interpolation….Pages 177-188