Weighted Sobolev theorem in Lebesgue spaces withvariable exponent: corrigendum

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Weighted Sobolev theorem in Lebesgue spaces withvariable exponent: corrigendum N. Samko

We fill in a gap discovered in the proof of Theorem A, on weighted Sobolev typeboundedness for potential operators in variable exponent Lebesgue spaces, in the pa-per of the authors ”Weighted Sobolev theorem in Lebesgue spaces with variable expo-nent”, J. Math. Anal. and Applic., 2007, vol. 335, No 1, 560-583. The proof remains thesame in the case where the Matuszewska-Orlich indices푚(푤)and푀(푤)of the weight푤are both positive or negative, but in the case where they have different signs, the proofneeds some additional arguments and requires a slightly different formulation of theresult.

DOI: https://armjmath.sci.am/index.php/ajm/article/view/69 Armenian Journal of Mathematics, 3(2) 92-97

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Keywords

Sobolev theorem, Hardy inequality, Lebesgue spaces with variable expo-nents, Riesz potentials, spherical potentials, Zygmund-Bary-Stechkin conditions

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