Rening the Submean Inequality for Subharmonic Functions

摘要

It is known that the composition of a convex, increasing functional with a subharmonic function is subharmonic. In this paper we show that the composition of a superquadratic functional with a subharmonic function is subharmonic, with a sharper submean inequality. It is further demonstrated that the composition of an increasing convex functional with a nonnegative superquadratic functional with a subharmonic function is subharmonic, with a sharper submean inequality.