Uniform geometric estimates for sublevel sets

Details Uniform geometric estimates for sublevel sets Uniform geometric estimates for sublevel sets

2009-09-04

arxiv.org/abs/0909.0875v1

Mathematics

Classical Analysis and ODEs

16 pages, 1 figure

Scientific paper

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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