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Bounds for Kakeya-type maximal operators associated with k-planes by Oberlin, Richard is a scholarly article available to read on EtoBox.

What is Bounds for Kakeya-type maximal operators associated with k-planes about?

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.

Author

Oberlin, Richard

Published

2005

Language

EN