A new characterization of holomorphic functions in the unit disk

V. V. Volchkov, Vit. V. Volchkov

Donetsk National University, 24, Universitetskaya str., Donetsk 83001

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.

UDC: 517.444

MSC: 43A45

Received: 22.12.2017
Revised: 11.03.2018
Accepted: 11.03.2018

Language: English

DOI: 10.15393/j3.art.2018.4690

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