Boundary values of functions in vector-valued Hardy spaces and geometry on Banach spaces
type: Item
instance of: scholarly article
title: Boundary values of functions in vector-valued Hardy spaces and geometry on Banach spaces
zbMATH Open document ID: 0658.46031
DOI: 10.1016/0022-1236(88)90123-1
author: Oscar Blasco
published in: Journal of Functional Analysis
publication date: 1988-01-01T00:00:00Z
review text: The spaces of boundary values of vector-valued functions in Hardy spaces defined by either holomorphic functions on the disk or harmonic functions with maximal function in \(L^ p\) are characterized in terms of vector- valued measures of bounded p-variation (sections 1 and 2). Also, the author extends to the case \(p=1\) a characterization of the Radon-Nikodym property based on the existence of limits at the boundary for harmonic functions with maximal function in \(L^ 1\). In the case \(0<p\leq 1\), the author proves that the UMD property is the necessary and sufficient condition to make the spaces defined by maximal function and by conjugate Poisson kernel coincide.
Mathematics Subject Classification ID: 46E40
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 46B22
zbMATH DE Number: 4075829
zbMATH Keywords: boundary values of vector-valued functions in Hardy spaces
zbMATH Keywords: vector-valued measures of bounded p-variation
zbMATH Keywords: Radon-Nikodym property
zbMATH Keywords: maximal function
zbMATH Keywords: UMD property
zbMATH Keywords: conjugate Poisson kernel
MaRDI profile type: Publication
full work available at URL: 0022-1236(88)90123-1
OpenAlex ID: W2051222651
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description: scientific article; zbMATH DE number 4075829