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

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Şahin S.

Banach Center Publications

2015

tom 107

nr 1

205-214

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.

Ograniczanie wyników

1 Banach Center Publications

1 Şahin S.

1 2015

Wyniki wyszukiwania

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