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

• Autorzy: Alexander V. Abanin , Pham Trong Tien
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 32C22: Embedding of analytic spaces
• 46B20: Geometry and structure of normed linear spaces
• 32K05: Banach analytic spaces
• 32C18: Topology of analytic spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2012
• Tom: 213
• Numer: 2
• Strony: 169-187

Daty

wydano

2012

Twórcy

autor

Alexander V. Abanin

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

autor

Pham Trong Tien

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

Identyfikatory

DOI

10.4064/sm213-2-4