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On a Lipschitz Variant of the Kakeya Maximal Function

Michael Lacey, Xiaochun Li

Published 2006-01-10, updated 2006-11-02Version 2

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.

Comments: 12 pages. The L^2 estimate for the maximal function in this paper is correct. A claimed L^p inequality, for 1<p<2, had an incomplete proof
Categories: math.CA
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