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Bergman spaces, Bloch spaces and integral means of \(p\)-harmonic functions. (English) Zbl 1470.31003

Summary: In this paper, we investigate the properties of Bergman 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.

MSC:

31C05 Harmonic, subharmonic, superharmonic functions on other spaces
46E15 Banach spaces of continuous, differentiable or analytic functions
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