Lipschitz-type and Bloch-type spaces of pluriharmonic mappings in a Hilbert space
type: Item
instance of: scholarly article
title: Lipschitz-type and Bloch-type spaces of pluriharmonic mappings in a Hilbert space
zbMATH Open document ID: 1396.31005
DOI: 10.1155/2017/9207645
author: Yong Liu
published in: Journal of Function Spaces
publication date: 2017-11-01T00:00:00Z
review text: The paper considers complex-valued pluriharmonic functions \(f\) on an infinite-dimensional Hilbert space \(E\), i.e., \(f=g+\bar h\) for holomorphic functions \(g\) and \(h\) on a domain in \(E\). First, the functions \(f\) satisfying \(|f(z)-f(w)|\leq C\omega(|z-w|)\) are characterized as those with the similar conditions separately on \(g\) and \(h\), or on \(|g|\) and \(|h|\); here \(\omega\) is a continuous function on \(\mathbb R_+\), \(\omega(0)=0\), such that \(\omega(t)/t\) is increasing. In addition, Bloch-type spaces of pluriharmonic functions on the unit ball of \(E\) are characterized in terms of the ratios \(|f(z)-f(w)|/|z-w|\).
Mathematics Subject Classification ID: 31C10
Mathematics Subject Classification ID: 46E25
zbMATH DE Number: 6802011
zbMATH Keywords: pluriharmonic functions on Hilbert spaces
zbMATH Keywords: Lipschitz class
zbMATH Keywords: Bloch class
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/9207645
OpenAlex ID: W2744338166
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description: scientific article; zbMATH DE number 6802011