On the boundedness of classical operators on weighted lorentz spaces |
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Authors: | Y Rakotondratsimba |
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Institution: | (1) Institut Polytechnique St. Louis Ecole de Physique et de Mathématiques Industrielles, 13, boulevard de l’Hautil, 95 092 Cergy-Pontoise Cedex, France |
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Abstract: | Conditions on weightsu(·),v(·) are given so that a classical operatorT sends the weighted Lorentz spaceL
Lrs
(vdx) intoL
pq
(udx). HereT is either a fractional maximal operatorM
α
or a fractional integral operatorI
α
or a Calderón-Zygmund operator. A characterization of this boundedness is obtained forM
α
andI
α
when the weights have some usual properties and max(r, s) ≤ min(p, q). |
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Keywords: | Maximal operators fractional integral Calderón-Zygmund operators weighted Lorentz spaces |
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