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A weighted inequality for the Kakeya maximal operator

Author: A. M. Vargas
Journal: Proc. Amer. Math. Soc. 120 (1994), 1101-1105
MSC: Primary 42B25
MathSciNet review: 1170548
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Abstract: Let $ {\mathcal{K}_\delta }$ be the Kakeya Maximal Operator defined as the supremum of averages over parallelepipeds of eccentricity $ \delta $. We show that $ {\mathcal{K}_\delta }$ satisfies $ \vert\vert{\mathcal{K}_\delta }f\vert{\vert _{{L^p}(\omega )}} \leqslant {C_{n... ...)^{{\alpha _n}}}\vert\vert f\vert{\vert _{{L^p}({\mathcal{K}_\delta }\omega )}}$ for all $ p \leqslant (n + 1)/2$ with some constants $ {C_{n,p}},\;{\alpha _n}$, independent of $ f$ and the weight $ \omega $.

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Keywords: Maximal functions, weighted inequalities
Article copyright: © Copyright 1994 American Mathematical Society

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