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arXiv · 1404.2690

The Kakeya maximal operator on the variable Lebesgue spaces

Hiroki Saito·Hitoshi Tanaka
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Abstract

We shall verify the Kakeya (Nikodym) maximal operator $K_{N}$, $N\gg 1$, is bounded on the variable Lebesgue space $L^{p(\cdot)}(\mathbb{R}^2)$ when the exponent function $p(\cdot)$ is $N$-modified locally log-Hölder continuous and log-Hölder continuous at infinity.

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Hiroki Saito, Hitoshi Tanaka. 2014-04-10. The Kakeya maximal operator on the variable Lebesgue spaces. https://arxiv.org/abs/1404.2690

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