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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Covering lemmas and the sharp function


Authors: Richard J. Bagby and Douglas S. Kurtz
Journal: Proc. Amer. Math. Soc. 93 (1985), 291-296
MSC: Primary 42B25; Secondary 46E30
MathSciNet review: 770539
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Abstract: We present some new measure-theoretic inequalities for families of cubes covering open sets in $ {{\mathbf{R}}^n}$ and use these inequalities to estimate the Hardy-Littlewood maximal function $ Mf$ in terms of the sharp function $ {f^\char93 }$.


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DOI: https://doi.org/10.1090/S0002-9939-1985-0770539-X
Keywords: $ {A_\infty }$ weight function, covering lemma, Hardy-Littlewood maximal function, sharp function
Article copyright: © Copyright 1985 American Mathematical Society