Projective Limits of Poletsky–Stessin Hardy Spaces

Abstract

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 [10], is isomorphic to the space H ∞ (D) of bounded holomorphic functions on D endowed with a special topology.To prove this we show that Carathéodory balls lie in approach regions, establish a sharp inequality for the Monge-Ampére 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 ∞ (D).

Intersection of harmonically weighted Dirichlet spaces

“…for every μ ∈ P. The purpose of this paper is to consider μ∈P D(μ), the intersection of D(μ) spaces with positive Borel probability measures μ. The properties and the applications of the intersection of Poletsky-Stessin Hardy spaces have been studied recently in [5,6].…”