Bounds for Kakeya-type maximal operators associated with k-planes
经典分析与常微分方程
2007-05-23 v1
摘要
A (d,k) set is a subset of R^d containing a translate of every k-dimensional plane. Bourgain showed that for k \geq k_{cr}(d), where k_{cr}(d) solves 2^{k_{cr}-1}+k_{cr} = d, every (d,k) set has positive Lebesgue measure. We give a short proof of this result which allows for an improved L^p estimate of the corresponding maximal operator, and which demonstrates that a lower value of k_{cr} could be obtained if improved mixed-norm estimates for the x-ray transform were known.
引用
@article{arxiv.math/0512377,
title = {Bounds for Kakeya-type maximal operators associated with k-planes},
author = {Richard Oberlin},
journal= {arXiv preprint arXiv:math/0512377},
year = {2007}
}
备注
9 pages. No figures