A characterization of the Cegrell classes and generalized $m$-capacities
Volume 121 / 2018
Annales Polonici Mathematici 121 (2018), 33-43
MSC: 32U15, 32U10, 32U20.
DOI: 10.4064/ap170728-26-1
Published online: 22 March 2018
Abstract
We give a new characterization of the classes $\mathcal {E}_m(\varOmega )$, $\mathcal {F}_m(\varOmega )$ and $\mathcal {F}_m^a(\varOmega )$ in terms of the $m$-capacity of sublevel sets. We also investigate the properties of the weighted relative $m$-extremal function $u_E$ associated to a subset $E\subset \varOmega $ and a function $u\in \mathcal {E}_m(\varOmega )$. We shall give a relationship between $u$ and the $C_{m,u}$-capacity of $E$.
