Geodesic
Painlevé null sets, dimension and compact embedding of weighted holomorphic spaces
Alexander V. Abanin1 ; Pham Trong Tien1
1Southern Federal University (SFU) Rostov-na-Donu 344090, The Russian Federation and Southern Institute of Mathematics (SIM) Vladikavkaz 362027, The Russian Federation
Studia Mathematica, Tome 213 (2012) no. 2, pp. 169-187
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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.
DOI : 10.4064/sm213-2-4
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

Alexander V. Abanin  1   ; Pham Trong Tien  1

1 Southern Federal University (SFU) Rostov-na-Donu 344090, The Russian Federation and Southern Institute of Mathematics (SIM) Vladikavkaz 362027, The Russian Federation 
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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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