A metric approach to sparse domination
Abstract
We present a general approach to sparse domination based on single-scale -improving as a key property. The results are formulated in the setting of metric spaces of homogeneous type and avoid completely the use of dyadic-probabilistic techniques as well as of Christ-Hyt\"onen-Kairema cubes. Among the applications of our general principle, we recover sparse domination of Dini-continuous Calder\'on-Zygmund kernels on spaces of homogeneous type, we prove a family of sparse bounds for maximal functions associated to convolutions with measures exhibiting Fourier decay, and we deduce sparse estimates for Radon transforms along polynomial submanifolds of .
Cite
@article{arxiv.2009.00336,
title = {A metric approach to sparse domination},
author = {José M. Conde Alonso and Francesco Di Plinio and Ioannis Parissis and Manasa N. Vempati},
journal= {arXiv preprint arXiv:2009.00336},
year = {2024}
}
Comments
36 pages, submitted for publication. V2: improvement of the main results Theorems A and B; uniform bound on the truncations is now required for some L^p unrelated to the sparse exponents; upgraded to Dini modulus of continuity; L^{p_j} improving assumption simplified. Applications are unchanged but verification is simplified