Inequalities for weighted Hardy operators in weighted variable exponent Lebesgue space with 0<p(x)<1

Abstract

Weighted inequalities are proved for the weighted Hardy operators and the weighted dual of the classical Hardy operator acting from one weighted variable exponent Lebesgue space L_p(.),_ω1(0, ∞) to another weighted variable exponent Lebesgue space L_p(.),_ω2(0, ∞) for 0 < p(x) ≤ q(x) < 1.