Parabolic Singular Integrals with Nonhomogeneous Kernels

2021/03/23 by Bortz, Simon, Hoffman, John, Hofmann, Steve +2 · 1 citation
#28A75 #42B20 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2103.12830

Abstract

We establish L² boundedness of all "nice" parabolic singular integrals on "Good Parabolic Graphs", aka \em regular Lip(1,1/2) graphs. The novelty here is that we include non-homogeneous kernels, which are relevant to the theory of parabolic uniform rectifiability. Previously, the third named author had treated the case of homogeneous kernels. The present proof combines the methods of that work (which in turn was based on methods described in Christ's CBMS lecture notes), with the techniques of Coifman-David-Meyer.

Cited by

• On Singular Integrals and Quantitative Rectifiability in Parabolic Space and the Heisenberg Group

Related

• Singular Integrals Associated to Hypersurfaces: L² Theory
• Singular integrals on C^1,α intrinsic graphs in step 2 Carnot groups
• A singular integral approach to the maximal L^p regularity of parabolic equations
• Singular integrals on C^1,α regular curves in Carnot groups
• L^p-parabolic regularity and non-degenerate Ornstein-Uhlenbeck type operators