Mathematics

On one application of the Zygmund–Marcinkiewicz theorem

M. V. Kukushkin<sup>ab

a</sup> Moscow State University of Civil Engineering, 26 Yaroslavskoe Shosse, Moscow 129337, Russia
^b Kabardino-Balkarian Scientific Center, 2 Balkarov Street, Nalchik 360051, Russia

Abstract: In this paper we aim to generalize results obtained in the framework of fractional calculus due to reformulating them in terms of operator theory. In its own turn, the achieved generalization allows us to spread the obtained technique on practical problems connected with various physical and chemical processes. More precisely, a class of existence and uniqueness theorems is covered, the most remarkable representative of which is the existence and uniqueness theorem for the Abel equation in a weighted Lebesgue space. The method of proof corresponding to the uniqueness part is worth noticing separately: it reveals properties of the operator as well as properties of the space into which it acts and emphasizes their relationship.

Keywords: Riemann–Liouville operator, Abel equation, Jacobi polynomial, weighted Lebesgue space.

UDC: 517.983.2

Received: 31.01.2020
Revised: 18.07.2020
Accepted: 30.08.2020

Language: English

DOI: 10.25587/SVFU.2020.31.27.004

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