On Some Weighted Classes of m-Subharmonic Functions
In this paper, we study the class $\mathcal{E}_m(\Omega)$ of $m$-subharmonic functions introduced by Lu in [18]. We prove that the convergence of the Hessian measures is deduced from the convergence in $m$-capacity for the functions that belong to $\mathcal{E}_m(\Omega)$ satisfying certain additiona...
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| Date: | 2024 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2024
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| Subjects: | |
| Online Access: | https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1057 |
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| Journal Title: | Journal of Mathematical Physics, Analysis, Geometry |
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Journal of Mathematical Physics, Analysis, Geometry| Summary: | In this paper, we study the class $\mathcal{E}_m(\Omega)$ of $m$-subharmonic functions introduced by Lu in [18]. We prove that the convergence of the Hessian measures is deduced from the convergence in $m$-capacity for the functions that belong to $\mathcal{E}_m(\Omega)$ satisfying certain additional properties. Then we extend those results to the class $\mathcal{E}_{m,\chi}(\Omega)$ that depends on a given increasing real function $\chi$. A complete characterization of those classes using the Hessian measure is given as well as a subextension theorem relative to $\mathcal{E}_{m,\chi}(\Omega)$.
Mathematical Subject Classification 2020: 32W20, 32U05, 32U15, 32U40 |
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