Pointwise and Weighted Hessian Estimates for Kolmogorov-Fokker-Planck type operators

2022/05/30 by Ghosh, Abhishek, Tewary, Vivek
#35B45 #35K65 #35K70 #46E30 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2205.15069

Abstract

In this article, we obtain hessian estimates for Kolmogorov-Fokker-Planck operators in non-divergence form in several Banach function spaces. Our approach relies on a representation formula and newly developed sparse domination techniques in Harmonic Analysis. Our result when restricted to weighted Lebesgue spaces yields sharp quantitative hessian estimates for the Kolmogorov-Fokker-Planck operators.

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