Bergman spaces, Bloch spaces and integral means of p-harmonic functions
Bull. Korean Math. Soc.
Published online November 4, 2020
Xi Fu and Jinjing Qiao
Shanghai Polytechnic University, Hebei University
Abstract : In this paper, we investigate the properties of Bergman spaces,
Bloch spaces and integral means of $p$-harmonic functions on the
unit ball in $R^n$. Firstly, we offer some Lipschitz-type and
double integral characterizations for Bergman space
$\mathcal{A}_\gamma^k$. Secondly, we characterize Bloch space
$\mathcal{B}_\omega^\alpha$ in terms of weighted Lipschitz
conditions and $BMO$ functions. Finally, a Hardy-Littlewood type
theorem for integral means of $p$-harmonic functions is established.
Keywords : p-harmonic function, Bergman space, Bloch space, integral mean.
MSC numbers : 32A18, 31B05, 30C65
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