Duality for Hardy Spaces in Domains of $$\mathbb {C}^n$$ C n and Some Applications

Autor: Victor Gotlib, Alekos Vidras, Lev Aizenberg
Rok vydání: 2013
Předmět:
Zdroj: Complex Analysis and Operator Theory. 8:1341-1366
ISSN: 1661-8262
1661-8254
DOI: 10.1007/s11785-013-0337-z
Popis: Let $$\Omega \subset \mathbb {C}^n $$ be a bounded, strictly convex domain with $${{\mathcal {C}}}^3$$ boundary and $$\widetilde{\Omega }$$ be its dual complement. We prove that $$(H^p(\Omega ))^{\prime }=H^q(\widetilde{\Omega })$$ , where $$p>1$$ and $${1\over p}+{1\over q}=1$$ . 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 $$\Omega \subset \mathbb {C}^n$$ and which are representable by Carleman integral representation formula.
Databáze: OpenAIRE
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