Hardy type inequality with sharp constant for 0<p<1

Abstract

A power-weighted integral inequality with sharp constant for 0 < p < 1 was established by V.I. Burenkov for the Hardy operator (Hf)(x) = (1/x) ∫₋₀⁴⁶ f(t) dt for non-negative non-increasing functions f. In this work we consider a more general class of functions f and prove a new Hardy-type inequality with sharp constant for functions of this class.