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,∞), where0<p<∞,0<q≤∞,1<θ≤∞,u,w, andvare weight functions on(0,∞). Some fairly new discretizing and antidiscretizing techniques of independent interest are used.
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