Painlevé null sets, dimension and compact embedding of weighted holomorphic spaces

Alexander V. Abanin, and Pham Trong Tien. "Painlevé null sets, dimension and compact embedding of weighted holomorphic spaces." Studia Mathematica 213.2 (2012): 169-187. <http://eudml.org/doc/285903>.

@article{AlexanderV2012,
abstract = {We obtain, in terms of associated weights, natural criteria for compact embedding of weighted Banach spaces of holomorphic functions on a wide class of domains in the complex plane. Our study is based on a complete characterization of finite-dimensional weighted spaces and canonical weights for them. In particular, we show that for a domain whose complement is not a Painlevé null set each nontrivial space of holomorphic functions with O-growth condition is infinite-dimensional.},
author = {Alexander V. Abanin, Pham Trong Tien},
journal = {Studia Mathematica},
keywords = {weighted Banach spaces of holomorphic functions; compact embedding; Painlevé null set},
language = {eng},
number = {2},
pages = {169-187},
title = {Painlevé null sets, dimension and compact embedding of weighted holomorphic spaces},
url = {http://eudml.org/doc/285903},
volume = {213},
year = {2012},
}

TY - JOUR
AU - Alexander V. Abanin
AU - Pham Trong Tien
TI - Painlevé null sets, dimension and compact embedding of weighted holomorphic spaces
JO - Studia Mathematica
PY - 2012
VL - 213
IS - 2
SP - 169
EP - 187
AB - We obtain, in terms of associated weights, natural criteria for compact embedding of weighted Banach spaces of holomorphic functions on a wide class of domains in the complex plane. Our study is based on a complete characterization of finite-dimensional weighted spaces and canonical weights for them. In particular, we show that for a domain whose complement is not a Painlevé null set each nontrivial space of holomorphic functions with O-growth condition is infinite-dimensional.
LA - eng
KW - weighted Banach spaces of holomorphic functions; compact embedding; Painlevé null set
UR - http://eudml.org/doc/285903
ER -