On a capacitary strong type inequality and related capacitary estimates

TL;DR

This paper proves a new capacitary inequality related to Maz'ya's work, providing equivalent norms for Choquet integrals and deriving bounds for the Hardy-Littlewood maximal function in a sublinear context.

Contribution

It introduces a Maz'ya type capacitary inequality that addresses a special case of Adams' conjecture, linking capacities with Choquet integrals and maximal function bounds.

Findings

Established a Maz'ya type capacitary inequality

Derived equivalent norms for Choquet integrals

Obtained bounds for the Hardy-Littlewood maximal function

Abstract

We establish a Maz'ya type capacitary inequality which resolves a special case of a conjecture by David R. Adams. As a consequence, we obtain several equivalent norms for Choquet integrals associated to Bessel or Riesz capacities. This enables us to obtain bounds for the Hardy-Littlewood maximal function in a sublinear setting.