Generalized Hardy spaces
type: Item
instance of: scholarly article
title: Generalized Hardy spaces
zbMATH Open document ID: 1204.42030
author: Alexandre Almeida
author: António M. Caetano
publication date: 2010-11-17T00:00:00Z
review text: As is known, there are various ways to define Hardy spaces, especially in the multi-dimensional setting. One of such approaches is the maximal function approach. Using it, the authors introduce a family of Hardy spaces based on a functional parameter. Many known Hardy and Hardy-Lorentz type spaces are particular cases. The authors then study interpolation properties of the introduced spaces by the real method with function parameter. Further, they prove the continuity of the Fourier transform of the functions from these spaces and give a control for its growth. They also establish a Hardy-Littlewood-Sobolev type theorem for the Riesz fractional integration and prove the boundedness of singular integral operators.
reviewed by: Elijah Liflyand
Mathematics Subject Classification ID: 42B30
Mathematics Subject Classification ID: 42B25
Mathematics Subject Classification ID: 46M35
Mathematics Subject Classification ID: 31B15
Mathematics Subject Classification ID: 42B20
zbMATH DE Number: 5816585
zbMATH Keywords: generalized Hardy spaces
zbMATH Keywords: maximal functions
zbMATH Keywords: Poisson kernel
zbMATH Keywords: interpolation with function parameter
zbMATH Keywords: Riesz potential
zbMATH Keywords: singular integral
MaRDI profile type: Publication
full work available at URL: s10114-010-8647-9
OpenAlex ID: W2052009382
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DOI: 10.1007/S10114-010-8647-9
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 5816585