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 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.b200367Published online November 4, 2020Printed 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) Downloads: Full-text PDF   Full-text HTML