Weighted inequalities for iterated Copson integral operators

2018/06/13 by Křepela, Martin, Pick, Luboš
#26D10 #46E30 #47B38 #47G10 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1806.04909

Abstract

We solve a long-standing open problem in theory of weighted inequalities concerning iterated Copson operators. We use a constructive approximation method based on a new discretization principle that is developed here. In result, we characterize all weight functions w,v,u on (0,∞) for which there exists a constant C such that the inequality (∫₀^∞(∫_t^∞ (∫_s^∞h(y) dy)^mu(s) ds)^(q)/(m)w(t) dt)^(1)/(q) ≤ C (∫₀^∞h(t)^pv(t) dt)^(1)/(p) holds for every non-negative measurable function h on (0,∞), where p,q and m are positive parameters. We assume that p≥ 1 but otherwise p,q and m are unrestricted.

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