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December 1999 An Estimate for the Kakeya Maximal Operator on Functions of Square Radial Type
Hitoshi TANAKA
Tokyo J. Math. 22(2): 391-398 (December 1999). DOI: 10.3836/tjm/1270041445

Abstract

The small Kakeya maximal operator, $M_{a,N}$, in $\mathbf{R}^d$ is defined by averages on cylinders with the width $a$ and the height $Na$. We show that the inequality $\lVert M_{a,N}f\rVert_d \leq C\log N\lVert f\rVert_d$ holds for the functions of square radialy type, where $C$ is a constant depending only on $d$.

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Hitoshi TANAKA. "An Estimate for the Kakeya Maximal Operator on Functions of Square Radial Type." Tokyo J. Math. 22 (2) 391 - 398, December 1999. https://doi.org/10.3836/tjm/1270041445

Information

Published: December 1999
First available in Project Euclid: 31 March 2010

zbMATH: 0959.42013
MathSciNet: MR1727882
Digital Object Identifier: 10.3836/tjm/1270041445

Rights: Copyright © 1999 Publication Committee for the Tokyo Journal of Mathematics

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Vol.22 • No. 2 • December 1999
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