Bergman spaces, Bloch spaces and integral means of $p$-harmonic functions
Bull. Korean Math. Soc. 2021 Vol. 58, No. 2, 481-495
https://doi.org/10.4134/BKMS.b200367
Published online November 4, 2020
Printed March 31, 2021
Xi Fu, Jinjing Qiao
Shanghai Polytechnic University; Hebei University
Abstract : In this paper, we investigate the properties of Bergman \linebreak spaces, Bloch spaces and integral means of $p$-harmonic functions on the unit ball in $\mathbb{R}^n$. 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 : Primary 32A18, 31B05, 30C65
Supported by : This work was partly supported by the Foundation of Shanghai Polytechnic University(No. EGD20XQD15) and NSF of Hebei Province (No. A2018201033)
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