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On a Lipschitz Variant of the Kakeya Maximal Function

Michael Lacey·Xiaochun Li
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Abstract

In a prior work [Hilbert transform along smooth families of lines math.CA/0310345] the authors introduced a variant of the Kakeya maximal function associated with Lipschitz maps from the plane into the unit circle. In this paper, we improve the known estimates for this maximal operator--and raise the conjecture that the bounds established are optimal.

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Michael Lacey, Xiaochun Li. 2006-11-02. On a Lipschitz Variant of the Kakeya Maximal Function. https://arxiv.org/abs/math/0601213

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