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Weighted Inequalities for Hardy--Steklov Operators

  Published:2007-04-01
 Printed: Apr 2007
  • A. L. Bernardis
  • F. J. MartĂ­n-Reyes
  • P. Ortega Salvador
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Abstract

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 $0
Keywords: Hardy--Steklov operator, weights, inequalities Hardy--Steklov operator, weights, inequalities
MSC Classifications: 26D15, 46E30, 42B25 show english descriptions Inequalities for sums, series and integrals
Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Kothe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Maximal functions, Littlewood-Paley theory
26D15 - Inequalities for sums, series and integrals
46E30 - Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Kothe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
42B25 - Maximal functions, Littlewood-Paley theory
 

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