English

Sparse domination via the Calder\'on-Zygmund decomposition: the example of Dini-smooth kernels

Classical Analysis and ODEs 2025-09-10 v1

Abstract

In this expository article, we briefly survey the main known schemes of proof of sparse domination principles within harmonic analysis. We then use the one based on the Calder\'on-Zygmund decomposition to prove a dual sparse domination estimate for Calder\'on-Zymgund operators with Dini-smooth kernels, with an eye on the difficulties that arise when trying to transfer the argument to spaces with nondoubling measures.

Keywords

Cite

@article{arxiv.2509.07659,
  title  = {Sparse domination via the Calder\'on-Zygmund decomposition: the example of Dini-smooth kernels},
  author = {Fernando Ballesta-Yagüe and José M. Conde-Alonso},
  journal= {arXiv preprint arXiv:2509.07659},
  year   = {2025}
}