On a Lipschitz Variant of the Kakeya Maximal Function

Details On a Lipschitz Variant of the Kakeya Maximal Function On a Lipschitz Variant of the Kakeya Maximal Function

2006-01-10

arxiv.org/abs/math/0601213v2

Mathematics

Classical Analysis and ODEs

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 inco

Scientific paper

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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