Weighted Hardy spaces
type: Item
instance of: scholarly article
title: Weighted Hardy spaces
zbMATH Open document ID: 0676.42021
author: Jan-Olov Strömberg
author: Alberto Torchinsky
published in: Lecture Notes in Mathematics
publication date: 1992-09-17T00:00:00Z
review text: The authors give the detailed version of their announcement in Bull. Am. Math. Soc., New Ser. 3, 1053-1056 (1980; Zbl 0452.43004) several results developed since then, and some applications. In Chapter 1 they introduce the notion of weighted measures in the general context of homogeneous spaces, including the theory of \(A_ p\) weights. Chapter 2 deals with the P. Jones decomposition of these weights, including the control of the doubling condition. In Chapter 3 they treat the properties of the sharp maximal functions and the local sharp maximal functions. Chapter 4 deals with the functions defined on the upper-half space \({\mathbb{R}}_+^{n+1}\), including the nontangential maximal functions and the area function. Then in Chapter 5 they discuss the extensions of a tempered distribution on \({\mathbb{R}}^ n\) to the upper- half space by means of convolutions with the dilates of Schwartz functions. In Chapter 6 they introduce the weighted Hardy spaces. They construct in Chapter 7 a dense class of functions for these spaces of distributions. In Chapter 8 they construct the atomic decomposition for these spaces and in Chapter 9 they describe an extension of the Fefferman \(H^ 1\) duality result. They construct the dual to the Hardy spaces in Chapter 10, and deal with the continuity of various singular integral and multiplier operators on these spaces in Chapter 11. Finally in Chapter 12 they show how the complex method of interpolation applies in these context.
Mathematics Subject Classification ID: 42B30
Mathematics Subject Classification ID: 42B25
Mathematics Subject Classification ID: 42-02
Mathematics Subject Classification ID: 42B20
Mathematics Subject Classification ID: 42B15
zbMATH DE Number: 43549
zbMATH Keywords: \(H^ p\) spaces weights
zbMATH Keywords: applications
zbMATH Keywords: weighted measures
zbMATH Keywords: homogeneous spaces
zbMATH Keywords: local sharp maximal functions
zbMATH Keywords: Schwartz functions
zbMATH Keywords: Hardy spaces
reviewed by: Kôzô Yabuta
MaRDI profile type: Publication
DOI: 10.1007/BFB0091154
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description: scientific article; zbMATH DE number 43549