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 Mat. Zametki, 2018, Volume 104, Issue 3, Pages 323–335 (Mi mz12107)

Analytic Description of the Spaces Dual to Spaces of Holomorphic Functions of Given Growth on Carathéodory Domains

A. V. Abaninab, T. M. Andreevab

a Southern Federal University, Rostov-on-Don

Abstract: The spaces dual to spaces of holomorphic functions of given growth on Carathéodory domains are described by using the Cauchy transform of functionals. A pseudoanalytic extension of such transforms to the whole plane is constructed, which makes it possible to remove convexity constrains and consider spaces determined by weights of general form, rather than only by those whose dependence on the distance from a point of the domain to its boundary is one-dimensional.

Keywords: weighted spaces of holomorphic functions, Cauchy transform of functionals, dual spaces.

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation ÌÊ-1056.2018.1 The work of the second-named author was supported by the Presidential Program for Support of Young Candidates of Sciences under grant MC-1056.2018.1.

DOI: https://doi.org/10.4213/mzm12107

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UDC: 517.5+517.9

Citation: A. V. Abanin, T. M. Andreeva, “Analytic Description of the Spaces Dual to Spaces of Holomorphic Functions of Given Growth on Carathéodory Domains”, Mat. Zametki, 104:3 (2018), 323–335

Citation in format AMSBIB
\Bibitem{AbaAnd18} \by A.~V.~Abanin, T.~M.~Andreeva \paper Analytic Description of the Spaces Dual to Spaces of Holomorphic Functions of Given Growth on Carath\'eodory Domains \jour Mat. Zametki \yr 2018 \vol 104 \issue 3 \pages 323--335 \mathnet{http://mi.mathnet.ru/mz12107} \crossref{https://doi.org/10.4213/mzm12107} \elib{http://elibrary.ru/item.asp?id=35410194}