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

@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 -