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

zbMATH Open1225.31008arXiv1007.4577MaRDI QIDQ3002130

Juhani Riihentaus

Publication date: 19 May 2011

Abstract: 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 ${mathbbR}^n$, $ngeq2$, are included. The following result of Gehring and Hallenbeck is classical: Every subharmonic function, defined and ${mathcalL}^p$-integrable for some $p$, $0<p<+infty$, on the unit disk $mathbbD$ of the complex plane $mathbbC$ is for almost all $heta$ of the form $o((1-|z|{)}^{-1/p})$, uniformly as $zo{e}^{iheta}$ in any Stolz domain. Recently both Pavlovi'c and Riihentaus have given related and partly more general results on domains of ${mathbbR}^n$, $ngeq2$. Now we extend one of these results to quasinearly subharmonic functions on locally uniformly homogeneous spaces.

Full work available at URL: https://arxiv.org/abs/1007.4577

zbMATH Keywords

locally uniformly homogeneous spacequasinearly subharmonic functions

Mathematics Subject Classification ID

Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Harmonic, subharmonic, superharmonic functions on other spaces (31C05) Other generalizations (nonlinear potential theory, etc.) (31C45)

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