On Boundedness of Weighted Hardy Operator in Lp and Regularity Condition

We give a new proof for power-type weighted Hardy inequality in the norms of generalized Lebesgue spaces L-p(.) (R-n). Assuming the logarithmic conditions of regularity in a neighborhood of zero and at infinity for the exponents p(x) <= = q(x), <= q(x), necessary and sufficient conditions are proved for the boundedness of the Hardy operator Hf(x) = integral(vertical bar y vertical bar