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In this paper author was proved the boundedness of the multidimensional Hardytype operator in weighted Lebesgue spaces with a variable exponent. As anapplication we prove the boundedness of certain sublinear operators on theweighted variable Lebesgue space. Note that the proof of multidimensional Hardytype operator in weighted Lebesgue spaces with a variable exponent don'tcontained any mistakes. But at the proving of the boundedness of certainsublinear operators on the weighted variable Lebesgue space Georgian colleaguesdiscovered a small but significant error in this paper. This result is assignedas Theorem 5 in noted paper. In other words, sufficient conditions for generalweights ensuring the validity of the two-weight strong type inequalities forsome sublinear operator was found. In this theorem the inequality (9) isn'ttrue. In this note we give the details of the correct argument. We presume thatthe reader is familiar with the contents and notation of our original paper. Atthe heart of our correction is the following Theorem which replaces Theorem 5.

Corrections to the paper "The boundedness of certain sublinear operator in the weighted variable Lebesgue spaces"