Maximal functions of plurisubharmonic functions

Abstract

We show that for nonnegative plurisubharmonic functions on the unit ball of $C^{n}$ the admissible maximal functions are dominated by the radial maximal functions in $L^{p}$-mean. This gives another characterization of the class $M^{p}$ of holomorphic functions and its invariance under the compositions by automorphisms of the unit ball. As a consequence of the invariance all onto endomorphisms of $M^{1}$ $(n=1)$ are characterized.