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arXiv · 2603.08186

Pointwise estimates for rough operators in a metric measure framework under some Ahlfors regularity conditions

Diego Chamorro·Anca-Nicoleta Marcoci·Liviu-Gabriel Marcoci
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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.

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Diego Chamorro, Anca-Nicoleta Marcoci, Liviu-Gabriel Marcoci. 2026-03-09. Pointwise estimates for rough operators in a metric measure framework under some Ahlfors regularity conditions. https://arxiv.org/abs/2603.08186

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