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

S. G. Samko ; S. M. Umarkhadzhiev

Matematičeskie zametki, Tome 93 (2013) no. 4, pp. 575-585.

Résumé

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.

Détail

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

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