Проблемы анализа (Apr 2018)

A NEW CHARACTERIZATION OF HOLOMORPHIC FUNCTIONS IN THE UNIT DISK

  • Volchkov Valerii V.,
  • Volchkov Vitalii V.

DOI
https://doi.org/10.15393/j3.art.2018.4690
Journal volume & issue
Vol. 7(25), no. 1
pp. 134 – 147

Abstract

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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