A weighted inequality for the Kakeya maximal operator
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- by A. M. Vargas PDF
- Proc. Amer. Math. Soc. 120 (1994), 1101-1105 Request permission
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 $||{\mathcal {K}_\delta }f|{|_{{L^p}(\omega )}} \leqslant {C_{n,p}}{(1/\delta )^{n/p - 1}}{(\log (1/\delta ))^{{\alpha _n}}}||f|{|_{{L^p}({\mathcal {K}_\delta }\omega )}}$ for all $p \leqslant (n + 1)/2$ with some constants ${C_{n,p}},\;{\alpha _n}$, independent of $f$ and the weight $\omega$.References
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Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 120 (1994), 1101-1105
- MSC: Primary 42B25
- DOI: https://doi.org/10.1090/S0002-9939-1994-1170548-0
- MathSciNet review: 1170548