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Weighted Norm Inequalities for the Local Sharp Maximal Function

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Abstract

A weighted norm inequality for the local sharp maximal function M# λf is proved. Our main result along with the extrapolation theorem by D. Cruz-Uribe and C. Perez is applied to obtaining several new weighted norm inequalities for maximal functions and singular integrals. Several open problems are given.

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  1. Department of Mathematics, Bar-Ilan University, Ramat-Gan 52900, Israel

    A.K. Lerner

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  1. A.K. Lerner
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Correspondence to A.K. Lerner.

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Lerner, A. Weighted Norm Inequalities for the Local Sharp Maximal Function. J. Fourier Anal. Appl. 10, 465–474 (2004). https://doi.org/10.1007/s00041-004-0987-3

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  • DOI: https://doi.org/10.1007/s00041-004-0987-3

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