Projective Limits of Poletsky–Stessin Hardy Spaces

In this paper we show that on a strongly pseudoconvex domain D the projective limit of all Poletsky–Stessin Hardy spaces (Formula presented.), introduced by Poletsky and Stessin in 2008, is isomorphic to the space (Formula presented.) 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 (Formula presented.) is (Formula presented.).