%0 Journal Article
%T Projective limits of Poletsky--Stessin Hardy spaces
%A Evgeny A. Poletsky
%J Mathematics
%D 2015
%I arXiv
%X In this paper we show that that on a strongly pseudoconvex domain $D$ the projective limit of all Poletsky--Stessin Hardy spaces $H^p_u(D)$, introduced in \cite{PS}, is isomorphic to the space $H^\infty(D)$ of bounded holomorphic functions on $D$ endowed with a special topology. To prove this we show that Carath\'eodory balls lie in approach regions, establish a sharp inequality for the Monge--Amp\'ere mass of the envelope of plurisubharmonic exhaustion functions and use these facts to demonstrate that the intersection of all Poletsky--Stessin Hardy spaces $H^p_u(D)$ is $H^\infty(D)$.
%U http://arxiv.org/abs/1503.00575v1