Poletsky–Stessin Hardy spaces on domains bounded by an analytic Jordan curve in ℂ

Abstract

We study Poletsky–Stessin Hardy spaces that are generated by continuous, subharmonic exhaustion functions on a domain , that is bounded by an analytic Jordan curve. Different from Poletsky and Stessin’s work these exhaustion functions are not necessarily harmonic outside of a compact set but have finite Monge–Ampère mass. We have showed that functions belonging to Poletsky–Stessin Hardy spaces have a factorization analogous to classical Hardy spaces and the algebra is dense in these spaces as in the classical case; however, contrary to the classical Hardy spaces, composition operators with analytic symbols on these Poletsky–Stessin Hardy spaces need not always be bounded