Cancellative sparse domination
Classical Analysis and ODEs
2026-05-12 v2 Probability
Abstract
We present a general sparse domination principle which respects the cancellative structure of the functions under study. We obtain sparse domination results in general measure spaces, including general martingale settings in one and two parameters, and in the Euclidean setting. In the one-parameter martingale setting, we obtain a sparse characterization of the norm. The proofs make critical use of precise level-set estimates for generalized versions of medians. Our results imply new, quantitatively sharp, weighted results for martingales and Calder\'on-Zygmund operators acting on spaces.
Keywords
Cite
@article{arxiv.2603.08446,
title = {Cancellative sparse domination},
author = {José M. Conde Alonso and Emiel Lorist and Guillermo Rey},
journal= {arXiv preprint arXiv:2603.08446},
year = {2026}
}