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arXiv · 0909.0875

Uniform geometric estimates for sublevel sets

Philip T. Gressman
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Abstract

This paper reconsiders the uniform sublevel set estimates of Carbery, Christ, and Wright (1999) and Phong, Stein, and Sturm (2001) from a geometric perspective. This perspective leads one to consider a natural collection of homogeneous, nonlinear differential operators which generalize mixed derivatives in $\R^d$. As a consequence, it is shown that, in the case of both of these previous works, improved uniform decay rates are possible in many situations.

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Philip T. Gressman. 2009-09-04. Uniform geometric estimates for sublevel sets. https://arxiv.org/abs/0909.0875

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