Various Types of Convergence of Sequences of Subharmonic Functions

Let $\upsilon_n(x)$ be a sequence of subharmonic functions in a domain $G\subset\mathbb{R}^m$. The conditions under which the convergence of $\upsilon_n(x)$, as a sequence of generalized functions, implies its convergence in the Lebesgue spaces $L_p(\gamma)$ are studied. The results similar to ours have been obtained earlier by Hörmander and also by Ghisin and Chouigui. Hörmander investigated the case where the measure $\gamma$ is some restriction of the $m$-dimensional Lebesgue measure. Grishin and Chouigui considered the case $m=2$. In this paper we consider the case $m>2$ and general measures $\gamma$.