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

Banach Center Publications (2015)

- Volume: 107, Issue: 1, page 205-214
- ISSN: 0137-6934

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topSibel Şahin. "Monge-Ampère measures and Poletsky-Stessin Hardy spaces on bounded hyperconvex domains." Banach Center Publications 107.1 (2015): 205-214. <http://eudml.org/doc/281945>.

@article{SibelŞahin2015,

abstract = {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.},

author = {Sibel Şahin},

journal = {Banach Center Publications},

language = {eng},

number = {1},

pages = {205-214},

title = {Monge-Ampère measures and Poletsky-Stessin Hardy spaces on bounded hyperconvex domains},

url = {http://eudml.org/doc/281945},

volume = {107},

year = {2015},

}

TY - JOUR

AU - Sibel Şahin

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

JO - Banach Center Publications

PY - 2015

VL - 107

IS - 1

SP - 205

EP - 214

AB - 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.

LA - eng

UR - http://eudml.org/doc/281945

ER -

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