Some New Iterated Hardy-Type Inequalities

Abstract

We characterize the validity of the Hardy-type inequality ∥∥∫s∞h(z)dz ∥p,u,(0,t) ∥q,w,(0, ∞)≤c ∥h∥θ,v(0,∞), where 0<p<∞, 0<q≤∞, 1<θ≤∞, u, w, and v are weight functions on (0,∞). Some fairly new discretizing and antidiscretizing techniques of independent interest are used.