Holomorphic martingales and interpolation between Hardy spaces
type: Item
instance of: scholarly article
title: Holomorphic martingales and interpolation between Hardy spaces
zbMATH Open document ID: 0796.60051
DOI: 10.1007/BF02788847
author: Paul F. X. Müller
published in: Journal d'Analyse Mathématique
publication date: 1994-04-18T00:00:00Z
review text: The concepts of holomorphic functions and holomorphic martingales introduced by Varopoulos are used to give simple probabilistic proofs of the following interpolation results. If a linear operator \(T\) is bounded both on \(H^ 1(T)\) and on \(H^ \infty(T)\), then it is bounded on \(H^ p(T)\) \((1<p<\infty)\) (P. W. Jones); if it is bounded both on \(H^ 1(T\times T)\) and on \(H^ 2(T\times T)\), then it is bounded on \(H^ p(T\times T)\) \((1<p<2)\) (S. Y. Chang, R. Fefferman) where \(T\) denotes the unit circle in the complex plane; and, moreover, if it is bounded both on \(H^ 1(R_ +^{n+1})\) and on \(L^ \infty(R_ +^{n+1})\), then it is bounded on \(H^ p(R_ +^{n+1})\) \((1<p<\infty)\) (N. M. Riviere, Y. Sagher), too. As the first step these theorems are verified for holomorphic martingale spaces and then they follow easily by a principle of transference.
reviewed by: Ferenc Weisz
Mathematics Subject Classification ID: 60G44
Mathematics Subject Classification ID: 46B70
Mathematics Subject Classification ID: 60G46
Mathematics Subject Classification ID: 42B30
zbMATH DE Number: 528679
zbMATH Keywords: holomorphic functions
zbMATH Keywords: Hardy spaces
zbMATH Keywords: Brownian motion
zbMATH Keywords: holomorphic martingales
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02788847
OpenAlex ID: W2016925972
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description: scientific article; zbMATH DE number 528679