Geodesic
A new characterization of holomorphic functions in the unit disk
Problemy analiza, Tome 7 (2018) no. 1, pp. 134-147

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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. 
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     author = {V. V. Volchkov and Vit. V. Volchkov},
     title = {A new characterization of holomorphic functions in the unit disk},
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V. V. Volchkov; Vit. V. Volchkov. A new characterization of holomorphic functions in the unit disk. Problemy analiza, Tome 7 (2018) no. 1, pp. 134-147. http://geodesic.mathdoc.fr/item/PA_2018_7_1_a8/