The Fefferman-Stein type inequality for the Kakeya maximal operator期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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The Fefferman-Stein type inequality for the Kakeya maximal operator

Authors:	Hitoshi Tanaka

Institution:	Department of Mathematics, Gakushuin University, 1-5-1 Mejiro, Toshima-ku, Tokyo 171-8588, Japan

Abstract:	Let $K_\delta$ , $0<\delta<<1$ , be the Kakeya maximal operator defined as the supremum of averages over tubes of the eccentricity $\delta$ . We shall prove the so-called Fefferman-Stein type inequality for $K_\delta$ , $\begin{displaymath}\Vert K_\delta f\Vert _{L^p(\mathbf R^d,w)} \le C_{d,p} (\fra... ...ta}))^{\alpha(d)} \Vert f\Vert _{L^p(\mathbf R^d,K_\delta w)}, \end{displaymath}$ in the range $(1<p\le(d^2-2)/(2d-3)$ , $d\ge3$ , with some constants $C_{d,p}$ and $\alpha(d)$ independent of and the weight .

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