On a Hardy Type General Weighted Inequality in Spaces Lp(.)

A Hardy type two-weighted inequality is investigated for the multidimensional Hardy operator in the norms of generalized Lebesgue spaces L-p(.). Equivalent necessary and sufficient conditions are found for the L-p(.) -> L-q(.) boundedness of the Hardy operator when exponents q(0) < p(0), q(infinity) < p(infinity). It is proved that the condition for such an inequality to hold coincides with the condition for the validity of two-weighted Hardy inequalities with constant exponents if we require of the exponents to be regular near zero and at infinity.