Geodesic
On the Regularization of a Multidimensional Integral Equation in Lebesgue Spaces with Variable Exponent
Matematičeskie zametki, Tome 93 (2013) no. 4, pp. 575-585

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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, Banach space, hypersingular operator, Hölder's inequality, Hardy–Stein–Weiss inequality.
Mots-clés : Lebesgue space with variable exponent 
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     author = {S. G. Samko and S. M. Umarkhadzhiev},
     title = {On the {Regularization} of a {Multidimensional} {Integral} {Equation} in {Lebesgue} {Spaces} with {Variable} {Exponent}},
     journal = {Matemati\v{c}eskie zametki},
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S. G. Samko; S. M. Umarkhadzhiev. On the Regularization of a Multidimensional Integral Equation in Lebesgue Spaces with Variable Exponent. Matematičeskie zametki, Tome 93 (2013) no. 4, pp. 575-585. http://geodesic.mathdoc.fr/item/MZM_2013_93_4_a8/