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Corpus ID: 119138525

Boundedness of Hardy-type operators with a kernel: integral weighted conditions for the case $0

@inproceedings{Kvrepela2016BoundednessOH,
title={Boundedness of Hardy-type operators with a kernel: integral weighted conditions for the case \$0},
author={Martin Kvrepela},
year={2016}
}

Let U : [0,∞)2 → [0,∞) be a measurable kernel satisfying: (i) U(x, y) is nonincreasing in x and nondecreasing in y; (ii) there exists a constant θ > 0 such that U(x, z) ≤ θ (U(x, y) + U(y, z)) for all 0 ≤ x < y < z < ∞; (iii) U(0, y) > 0 for all y > 0. Let 0 < q < 1 < p < ∞. We prove that the weighted inequality