On a Lipschitz Variant of the Kakeya Maximal Function
Classical Analysis and ODEs
2007-05-23 v2
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.
Cite
@article{arxiv.math/0601213,
title = {On a Lipschitz Variant of the Kakeya Maximal Function},
author = {Michael Lacey and Xiaochun Li},
journal= {arXiv preprint arXiv:math/0601213},
year = {2007}
}
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