Uniform geometric estimates for sublevel sets

2009/09/04 by Philip T. Gressman, Gressman, Philip T. · 1 citation
Mathematics · #Advanced Harmonic Analysis Research #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Geometry #Mathematics #Nonlinear Partial Differential Equations #math.CA

paper · pdf · doi:10.48550/arxiv.0909.0875

16 pages, 1 figure

arxiv created 2009/09/04 · openalex publication_date 2009/09/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• Best constants in Young's inequality, its converse, and its generalization to more than three functions
• The Newton polyhedron and oscillatory integral operators

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• Nondegeneracy and regularity of polynomial pushforwards

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