Various Types of Convergence of Sequences of Subharmonic Functions - Nguyen Van Quynh (Журнал математической физики, анализа, геометрии, 2015)
Let υn(x) be a sequence of subharmonic functions in a domain G is subset of Rm. The conditions under which the convergence of υn(x), as a sequence of generalized functions, implies its convergence in the Lebesgue spaces Lp(γ) 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 γ 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 γ.