On an inequality related to the radial growth of subharmonic functions

Abstract

It is a classical result that every subharmonic function, defined and â„’^p-integrable for some p, 0 < p < +∞, on the unit disk ð”» of the complex plane â„‚ is for almost all θ of the form o((1 − |ð“|)^−1/p), uniformly as ð“ → e^ð’¾Î¸ in any Stolz domain. Recently Pavlović gave a related integral inequality for absolute values of harmonic functions,
also defined on the unit disk in the complex plane. We generalize Pavlović‘s result to so called quasi-nearly subharmonic functions defined on rather general domains in â„^ð“ƒ, 𓃠≥ 2.