Some new classes of Hardy spaces
type: Item
instance of: scholarly article
title: Some new classes of Hardy spaces
zbMATH Open document ID: 0677.30030
DOI: 10.1016/0022-1236(89)90097-9
author: Yong-Zhou Chen
author: Ka-Sing Lau
published in: Journal of Functional Analysis
publication date: 1989-01-01T00:00:00Z
review text: The authors develop a Hardy space theory for certain function spaces, among them the spaces \[ B^ p=\{f\in L^ 1_{loc}({\mathbb{R}}):\quad \| f\| =\sup_{T\geq 1}[(2T)^{-1}\int^{T}_{-T}| f(t)|^ p dt]^{1/p}<\infty \}, \] 1\(<p<\infty\) (formerly considered by \textit{A. Beurling} [Ann. Inst. Fourier 14, No.2, 1-32 (1964; Zbl 0133.075)]), and the harmonic extension of their elements to the upper half-plane. Their results include a Burkholder-Gundy-Silverstein maximal function characterization of spaces related to the spaces \(B^ p\) above. Also considered are duality relations; for example, an analogue to the Fefferman-Stein theorem [\textit{C. Fefferman} and \textit{E. M. Stein}, Acta Math. 129, 137-193 (1972; Zbl 0257.46078)] on the duality between the classical Hardy space \(H^ 1\) and BMO is proved.
Mathematics Subject Classification ID: 30H05
Mathematics Subject Classification ID: 30D55
Mathematics Subject Classification ID: 46J15
zbMATH DE Number: 4109100
zbMATH Keywords: generalized Hardy spaces
reviewed by: Raymond Mortini
MaRDI profile type: Publication
full work available at URL: 0022-1236(89)90097-9
OpenAlex ID: W2006943907
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description: scientific article; zbMATH DE number 4109100