Abstract
In the class of harmonic functions, we study the properties of some integrodifferential operators generalizing the operators of fractional derivation in the sense of Hadamard and Hadamard-Marchaud. By way of application of the so-obtained properties, we consider some boundary value problems for the Laplace equation in the ball.
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Original Russian Text Copyright © 2012 Berdyshev A.S., Turmetov B.Kh., and Kadirkulov B.J.
The authors were partly supported by the Ministry of Science and Education of the Republic of Kazakhstan (Grant No 973).
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 53, No. 4, pp. 752–764, July–August, 2012.
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Berdyshev, A.S., Turmetov, B.K. & Kadirkulov, B.J. Some properties and applications of the integrodifferential operators of hadamard-marchaud type in the class of harmonic functions. Sib Math J 53, 600–610 (2012). https://doi.org/10.1134/S0037446612040039
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DOI: https://doi.org/10.1134/S0037446612040039