Painlevé null sets, dimension and compact embedding
of weighted holomorphic spaces
Studia Mathematica, Tome 213 (2012) no. 2, pp. 169-187
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
Keywords:
obtain terms associated weights natural criteria compact embedding weighted banach spaces holomorphic functions wide class domains complex plane study based complete characterization finite dimensional weighted spaces canonical weights particular domain whose complement painlev null set each nontrivial space holomorphic functions o growth condition infinite dimensional
Affiliations des auteurs :
Alexander V. Abanin 1 ; Pham Trong Tien 1
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author = {Alexander V. Abanin and Pham Trong Tien},
title = {Painlev\'e null sets, dimension and compact embedding
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journal = {Studia Mathematica},
pages = {169--187},
publisher = {mathdoc},
volume = {213},
number = {2},
year = {2012},
doi = {10.4064/sm213-2-4},
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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 SP - 169 EP - 187 VL - 213 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/sm213-2-4/ DO - 10.4064/sm213-2-4 LA - en ID - 10_4064_sm213_2_4 ER -
%0 Journal Article %A Alexander V. Abanin %A Pham Trong Tien %T Painlevé null sets, dimension and compact embedding of weighted holomorphic spaces %J Studia Mathematica %D 2012 %P 169-187 %V 213 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/sm213-2-4/ %R 10.4064/sm213-2-4 %G en %F 10_4064_sm213_2_4
Alexander V. Abanin; Pham Trong Tien. Painlevé null sets, dimension and compact embedding of weighted holomorphic spaces. Studia Mathematica, Tome 213 (2012) no. 2, pp. 169-187. doi: 10.4064/sm213-2-4
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