This article is cited in 4 papers

Conditions for the $L_{p,\lambda}$-Boundedness of the Riesz Potential Generated by the Gegenbauer Differential Operator

V. S. Guliev^ab, E. D. Ibragimov<sup>a

a</sup> Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences
^b Nikol'skii Mathematical Institute of Peoples’ Friendship University of Russia

Abstract: The results obtained in this paper refine and supplement a Hardy–Littlewood–Sobolev type theorem on the boundedness of the Riesz potential generated by the Gegenbauer differential operator on the spaces $L_{p,\lambda}$ proved in an earlier paper of the second author.

Keywords: Gegenbauer differential operator, Gegenbauer potential, generalized shift operator.

UDC: 517.518

Received: 30.05.2017
Revised: 24.07.2018

DOI: 10.4213/mzm11708

 English version: Mathematical Notes, 2019, 105:5, 674–683

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