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Problemy Analiza — Issues of Analysis, 2018, Volume 7(25), Issue 1, Pages 134–147
DOI: https://doi.org/10.15393/j3.art.2018.4690 (Mi pa224) 		 
A new characterization of holomorphic functions in the unit disk

V. V. Volchkov, Vit. V. Volchkov

Donetsk National University, 24, Universitetskaya str., Donetsk 83001
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DOI: https://doi.org/10.15393/j3.art.2018.4690
Abstract: We study the conditions under which a function satisfying a weighted Morera property for all hyperbolic circles of a fixed radius is holomorphic. We show that one of such conditions is the restriction on a speed of decrease of the difference between the function and its Cauchy type integral.
Keywords: Cauchy integral formula; holomorphy tests; Legendre functions; hyperbolic plane.
Received: 22.12.2017
Revised: 11.03.2018
Accepted: 11.03.2018
Bibliographic databases:
Document Type: Article
UDC: 517.444
MSC: 43A45
Language: English
Citation: V. V. Volchkov, Vit. V. Volchkov, “A new characterization of holomorphic functions in the unit disk”, Probl. Anal. Issues Anal., 7(25):1 (2018), 134–147
Citation in format AMSBIB
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\paper A new characterization of holomorphic functions in the unit disk
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\vol 7(25)
\issue 1
\pages 134--147
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\crossref{https://doi.org/10.15393/j3.art.2018.4690}
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