Weighted Sobolev theorem in Lebesgue spaces with variable exponent: corrigendum

Abstract

We fill in a gap discovered in the proof of Theorem A, on weighted Sobolev type boundedness for potential operators in variable exponent Lebesgue spaces, in the paper of the authors "Weighted Sobolev theorem in Lebesgue spaces with variable exponent", J. Math. Anal. and Applic., 2007, vol. 335, No 1, 560-583. The proof remains the same in the case where the Matuszewska-Orlich indices $m(w)$ and $M(w)$ of the weight $w$ are both positive or negative, but in the case where they have different signs, the proof needs some additional arguments and requires a slightly different formulation of the result.