Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Weighted rearrangement inequalities for local sharp maximal functions

Author: Andrei K. Lerner
Journal: Trans. Amer. Math. Soc. 357 (2005), 2445-2465
MSC (2000): Primary 42B20, 42B25
Published electronically: October 28, 2004
MathSciNet review: 2140445
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Abstract: Several weighted rearrangement inequalities for uncentered and centered local sharp functions are proved. These results are applied to obtain new weighted weak-type and strong-type estimates for singular integrals. A self-improving property of sharp function inequalities is established.

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Additional Information

Andrei K. Lerner
Affiliation: Department of Mathematics, Bar-Ilan University, 52900 Ramat Gan, Israel

Keywords: Weighted rearrangements, sharp maximal functions, singular integrals
Received by editor(s): September 10, 2003
Received by editor(s) in revised form: December 4, 2003
Published electronically: October 28, 2004
Article copyright: © Copyright 2004 American Mathematical Society