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 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 where the Monge-Ampère measure 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 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc107-0-15,
author = {Sibel \c Sahin},
title = {Monge-Amp\`ere measures and Poletsky-Stessin Hardy spaces on bounded hyperconvex domains},
journal = {Banach Center Publications},
volume = {104},
year = {2015},
pages = {205-214},
zbl = {06556713},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc107-0-15}
}
Sibel Şahin. Monge-Ampère measures and Poletsky-Stessin Hardy spaces on bounded hyperconvex domains. Banach Center Publications, Tome 104 (2015) pp. 205-214. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc107-0-15/