Monge–Ampère measures and Poletsky–Stessin Hardy spaces on bounded hyperconvex domains
Tom 107 / 2015
Streszczenie
Poletsky–Stessin Hardy (PS–Hardy) spaces are the natural generalizations of classical Hardy spaces of the unit disc to general bounded, hyperconvex domains. On a bounded hyperconvex domain , the PS–Hardy space H^{p}_{u}(\Omega) is generated by a continuous, negative, plurisubharmonic exhaustion function u of the domain. Poletsky and Stessin considered the general properties of these spaces and mainly concentrated on the spaces H^{p}_{u}(\Omega) where the Monge–Ampère measure (dd^{c}u)^{n} has compact support for the associated exhaustion function u. In this study we consider PS–Hardy spaces in two different settings. In one variable case we examine PS–Hardy spaces that are generated by exhaustion functions with finite Monge–Ampère mass but (dd^{c}u)^{n} does not necessarily have compact support. For n \gt 1, we focus on PS–Hardy spaces of complex ellipsoids which are generated by specific exhaustion functions. In both cases we will give results regarding the boundary value characterization and polynomial approximation.