We give an elementary approach which allows us to evaluate Seip's conditions characterizing interpolating and sampling sequences in weighted Bergman spaces of infinite order for a wide class of weights depending on the distance to the boundary of the domain. Our results also give some information on cases not covered by Seip's theory. Moreover, we obtain new criteria for weights to be essential.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap79-3-3,
author = {Pawe\l\ Doma\'nski and Mikael Lindstr\"om},
title = {Sets of interpolation and sampling for weighted Banach spaces of holomorphic functions},
journal = {Annales Polonici Mathematici},
volume = {79},
year = {2002},
pages = {233-264},
zbl = {1060.30045},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap79-3-3}
}
Paweł Domański; Mikael Lindström. Sets of interpolation and sampling for weighted Banach spaces of holomorphic functions. Annales Polonici Mathematici, Tome 79 (2002) pp. 233-264. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap79-3-3/