Pointwise estimates for rough operators in a metric measure framework under some Ahlfors regularity conditions
Functional Analysis
2026-03-10 v1
Abstract
We establish a new pointwise estimate for a class of rough operators in the setting of metric measure spaces endowed with a measure which is Ahlfors regular. This pointwise inequality can be divided in two steps: the first one relies in a subrepresentation formula that involves a modified Riesz potential and the upper gradient of the function considered and the second step gives a pointwise control of the Riesz potential in terms of a maximal function and a Morrey norm. We also investigate a family of functional inequalities that can be deduced from this pointwise estimate.
Keywords
Cite
@article{arxiv.2603.08186,
title = {Pointwise estimates for rough operators in a metric measure framework under some Ahlfors regularity conditions},
author = {Diego Chamorro and Anca-Nicoleta Marcoci and Liviu-Gabriel Marcoci},
journal= {arXiv preprint arXiv:2603.08186},
year = {2026}
}