Weighted Hardy Spaces / by Jan-Olov Strömberg, Alberto Torchinsky.

Format:

Book

Author/Creator:

Strömberg, Jan-Olov, author.

Torchinsky, Alberto, author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 1381.

Lecture Notes in Mathematics, 0075-8434 ; 1381

Language:

English

Subjects (All):

Geometry.

Local Subjects:

Geometry.

Physical Description:

1 online resource (VIII, 200 pages).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1989.

System Details:

text file PDF

Summary:

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.

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.

Other Format:

Printed edition:

ISBN:

9783540462071

Access Restriction:

Restricted for use by site license.