In this note we consider radially symmetric plurisubharmonic functions and the complex Monge-Ampère operator. We prove among other things a complete characterization of unitary invariant measures for which there exists a solution of the complex Monge-Ampère equation in the set of radially symmetric plurisubharmonic functions. Furthermore, we prove in contrast to the general case that the complex Monge-Ampère operator is continuous on the set of radially symmetric plurisubharmonic functions. Finally we characterize radially symmetric plurisubharmonic functions among the subharmonic ones using merely the laplacian.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap106-0-1,
author = {Per \AA hag and Rafa\l\ Czy\.z and Leif Persson},
title = {Radially symmetric plurisubharmonic functions},
journal = {Annales Polonici Mathematici},
volume = {105},
year = {2012},
pages = {1-17},
zbl = {1266.32047},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap106-0-1}
}
Per Åhag; Rafał Czyż; Leif Persson. Radially symmetric plurisubharmonic functions. Annales Polonici Mathematici, Tome 105 (2012) pp. 1-17. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap106-0-1/