Capacitary Maximal Inequalities and Applications

You-Wei Benson Chen, Keng Hao Ooi, Daniel Spector

In this paper we introduce capacitary analogues of the Hardy-Littlewood maximal function, \begin{align*} \mathcal{M}_C(f)(x):= \sup_{r>0} \frac{1}{C(B(x,r))} \int_{B(x,r)} |f|\;dC,…