Tsukuba Journal of Mathematics

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.

Article information

Source
Tsukuba J. Math., Volume 16, Number 1 (1992), 11-18.

Dates
First available in Project Euclid: 30 May 2017

https://projecteuclid.org/euclid.tkbjm/1496161827

Digital Object Identifier
doi:10.21099/tkbjm/1496161827

Mathematical Reviews number (MathSciNet)
MR1178662

Zentralblatt MATH identifier
0770.31007

Citation

Kim, Hong Oh; Park, Yeon Yong. Maximal functions of plurisubharmonic functions. Tsukuba J. Math. 16 (1992), no. 1, 11--18. doi:10.21099/tkbjm/1496161827. https://projecteuclid.org/euclid.tkbjm/1496161827