English

Parabolic Singular Integrals with Nonhomogeneous Kernels

Classical Analysis and ODEs 2025-06-05 v2 Analysis of PDEs

Abstract

We establish L2L^2 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.

Keywords

Cite

@article{arxiv.2103.12830,
  title  = {Parabolic Singular Integrals with Nonhomogeneous Kernels},
  author = {Simon Bortz and John Hoffman and Steve Hofmann and Jose-Luis Luna Garcia and Kaj Nystrom},
  journal= {arXiv preprint arXiv:2103.12830},
  year   = {2025}
}
R2 v1 2026-06-24T00:29:28.876Z