Duality for Hardy Spaces in Domains of ℂn and Some Applications

Lev Aizenberg; Victor Gotlib; Alekos Vidras

doi:10.1007/s11785-013-0337-z

Duality for Hardy Spaces in Domains of ℂⁿ and Some Applications

Lev Aizenberg, Victor Gotlib, Alekos Vidras

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

Let Ω ⊂ ℂⁿ be a bounded, strictly convex domain with C³ boundary and Ω̃ be its dual complement. We prove that (H^p(Ω))_″ = H^p(Ω̃), where p > 1 and 1/p + 1/q = 1. As an application of the above results we give the precise description of the dual space of the space of holomorphic functions defined in a special type of domains Ω ⊂ ℂⁿ and which are representable by Carleman integral representation formula.

Original language	English
Pages (from-to)	1341-1366
Number of pages	26
Journal	Complex Analysis and Operator Theory
Volume	8
Issue number	6
DOIs	https://doi.org/10.1007/s11785-013-0337-z
State	Published - Aug 2014

Keywords

Dual complement
Duality

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abstract = "Let Ω ⊂ ℂn be a bounded, strictly convex domain with C3 boundary and {\~Ω} be its dual complement. We prove that (Hp(Ω))″ = Hp({\~Ω}), where p > 1 and 1/p + 1/q = 1. As an application of the above results we give the precise description of the dual space of the space of holomorphic functions defined in a special type of domains Ω ⊂ ℂn and which are representable by Carleman integral representation formula.",

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N2 - Let Ω ⊂ ℂn be a bounded, strictly convex domain with C3 boundary and Ω̃ be its dual complement. We prove that (Hp(Ω))″ = Hp(Ω̃), where p > 1 and 1/p + 1/q = 1. As an application of the above results we give the precise description of the dual space of the space of holomorphic functions defined in a special type of domains Ω ⊂ ℂn and which are representable by Carleman integral representation formula.

AB - Let Ω ⊂ ℂn be a bounded, strictly convex domain with C3 boundary and Ω̃ be its dual complement. We prove that (Hp(Ω))″ = Hp(Ω̃), where p > 1 and 1/p + 1/q = 1. As an application of the above results we give the precise description of the dual space of the space of holomorphic functions defined in a special type of domains Ω ⊂ ℂn and which are representable by Carleman integral representation formula.

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KW - Duality

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Duality for Hardy Spaces in Domains of ℂⁿ and Some Applications

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Keywords

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