On an inequality related to the radial growth of quasinearly subharmonic functions in locally uniformly homogeneous spaces

Details On an inequality related to the radial growth of quasinearly subharmonic functions in locally uniformly homogeneous spaces On an inequality related to the radial growth of quasinearly subharmonic functions in locally uniformly homogeneous spaces

2010-07-26

arxiv.org/abs/1007.4577v2

Journal of Mathematical Sciences: Advances and Applications, 6, No. 1 (2010), 17-40

Mathematics

Analysis of PDEs

10 pages, conference talk at the International Conference on Complex Analysis in Memory of A.A. Gol'dberg (1930-2008), Lviv, M

Scientific paper

We begin by recalling the definition of nonnegative quasinearly subharmonic functions on locally uniformly homogeneous spaces. Recall that these spaces and this function class are rather general: among others subharmonic, quasisubharmonic and nearly subharmonic functions on domains of Euclidean spaces ${\mathbb{R}}^n$, $n\geq 2$, are included. The following result of Gehring and Hallenbeck is classical: Every subharmonic function, defined and ${\mathcal{L}}^p$-integrable for some $p$, $0

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