S. G. Samko, S. M. Umarkhadzhiev, “On the Regularization of a Multidimensional Integral Equation in Lebesgue Spaces with Variable Exponent”, Mat. Zametki, 2013, Volume 93, Issue 4,Pages <nobr>575

This article is cited in 3 papers

On the Regularization of a Multidimensional Integral Equation in Lebesgue Spaces with Variable Exponent

S. G. Samko^a, S. M. Umarkhadzhiev^b

^a University of Algarve
^b Chechen State University

Abstract: A multidimensional integral equation of the first kind with potential-type kernel of small order in spaces of summable functions of variable order is reduced to an equation of the second kind.

Keywords: multidimensional integral equation of the first (second) kind, regularization of an integral equation, Lebesgue space with variable exponent, Banach space, hypersingular operator, Hölder's inequality, Hardy–Stein–Weiss inequality.

UDC: 517.968

Received: 27.05.2010
Revised: 15.12.2012

DOI: 10.4213/mzm8786