Weighted Sobolev theorem in Lebesgue spaces withvariable exponent: corrigendum

N. Samko

Received N/A; revised N/A; accepted N/A

This work is licensed under Creative Commons Attribution–NonCommercial International License (CC BY-NC 4.0).

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.

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Weighted Sobolev theorem in Lebesgue spaces withvariable exponent: corrigendum

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