On an Inequality Related to the Radial Growth of Subharmonic Functions

It is a classical result that every subharmonic function, defined and L p-integrable for some p, 0 < p < +∞, on the unit disk D of the complex plane C is for almost all θ of the form o((1− |z|)−1/p), uniformly as z → eiθ 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 Rn, n ≥ 2.