Asymptotic behaviour of means of nonpositive M-subharmonic functions

Author
M. A. Voitovych
Ivan Franko National University of Lviv, Lviv, Ukraine
Abstract
We describe growth and decrease of $p$th means, $1\leq p\leq\frac{2n-1}{2(n-1)}$, of nonpositive $\mathcal{M}$-subharmonic functions in the unit ball in $\mathbb{C}^n$ in terms of smoothness properties of a measure. As consequence we obtain a haracterization of asumptotic behaviour for means of Poisson integrals in the unit ball defined by a positive measure.
Keywords
M-subharmonic function; M-harmonic function; Green potential; unit ball; invariant Laplacian; Riesz measure
DOI
doi:10.15330/ms.47.1.20-26
Reference
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Pages
20-26
Volume
47
Issue
1
Year
2017
Journal
Matematychni Studii
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