Monge-Ampère measures and Poletsky-Stessin Hardy spaces on bounded hyperconvex domains

• Autorzy: Sibel Şahin
• Języki publikacji: EN

Abstrakty

EN

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 Ω, the PS-Hardy space $H^{p}_{u}(Ω)$ 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 $H^{p}_{u}(Ω)$ 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 > 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.

Kategorie tematyczne

• 32C15: Complex spaces
• 47B33: Composition operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2015
• Tom: 107
• Numer: 1
• Strony: 205-214

Daty

wydano

2015

Twórcy

autor

Sibel Şahin

• Faculty of Engineering, Natural and Mathematical Sciences Department, Özyeğin University, Istanbul, Turkey

Identyfikatory

DOI

10.4064/bc107-0-15