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Journal of Function Spaces
Volume 2017 (2017), Article ID 9207645, 6 pages
https://doi.org/10.1155/2017/9207645
Research Article

Lipschitz-Type and Bloch-Type Spaces of Pluriharmonic Mappings in a Hilbert Space

Department of Mathematics, Shaoxing College of Arts and Sciences, Shaoxing 312000, Zhejiang Province, China

Correspondence should be addressed to Yong Liu; moc.361@2891udsgnoyuil

Received 12 May 2017; Accepted 11 July 2017; Published 7 August 2017

Academic Editor: Ruhan Zhao

Copyright © 2017 Yong Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We investigate some properties of pluriharmonic mappings in an infinite dimensional complex Hilbert space. Several characterizations for pluriharmonic mappings to be in Lipschitz-type and Bloch-type spaces are given, which are generalizations of the corresponding known ones for holomorphic functions with several complex variables.