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A characterization of the Cegrell classes and generalized $m$-capacities

Volume 121 / 2018

Van Thien Nguyen 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 $E$.

Authors

  • Van Thien NguyenInstitute of Mathematics
    Jagiellonian University
    Łojasiewicza 6
    30-348 Kraków, Poland
    e-mail

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