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# Weighted Inequalities for Hardy--Steklov Operators

Published:2007-04-01
Printed: Apr 2007
• A. L. Bernardis
• F. J. Martín-Reyes
We characterize the pairs of weights $(v,w)$ for which the operator $Tf(x)=g(x)\int_{s(x)}^{h(x)}f$ with $s$ and $h$ increasing and continuous functions is of strong type $(p,q)$ or weak type $(p,q)$ with respect to the pair $(v,w)$ in the case $0  Keywords: Hardy--Steklov operator, weights, inequalities  MSC Classifications: 26D15 - Inequalities for sums, series and integrals 46E30 - Spaces of measurable functions ($L^p\$-spaces, Orlicz spaces, Kothe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 42B25 - Maximal functions, Littlewood-Paley theory