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math.FA2023
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,…
math.FA2023
Some Remarks on Capacitary Integrals and Measure Theory
Augusto C. Ponce, Daniel Spector
We present results for Choquet integrals with minimal assumptions on the monotone set function through which they are defined. They include the equivalence of sublinearity and stro…