WEIGHTED HARDY-TYPE INEQUALITIES ON THE CONE OF QUASI-CONCAVE FUNCTIONS

摘要

The paper is devoted to the study of weighted Hardy-type inequalities on the cone of quasi-concave functions, which is equivalent to the study of the boundedness of the Hardy operator between the Lorentz Γ-spaces. For described inequalities we obtain necessary and sufficient conditions to hold for parameters q ≥ 1, p > 0 and sufficient conditions for the rest of the range of parameters.