Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2014; 51(4): 1195-1204

Printed July 1, 2014

https://doi.org/10.4134/BKMS.2014.51.4.1195

Copyright © The Korean Mathematical Society.

Volume integral means of harmonic functions on smooth boundary domains

Kyesook Nam and Inyoung Park

Seoul National University, Pohang University of Science and Technology

Abstract

We newly define the volume integral means of harmonic functions to characterize the weighted harmonic Bergman spaces. It is based on Xiao and Zhu's results on holomorphic Bergman spaces.

Keywords: volume mean integral, harmonic Bergman spaces, smooth boundary domains in $\mathbf{R}^n$

MSC numbers: Primary 31B05, 32A35, 32A36; Secondary 32A50

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