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...
Збережено в:
| Дата: | 2024 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2024
|
| Теми: | |
| Онлайн доступ: | https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1057 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Journal of Mathematical Physics, Analysis, Geometry |
Репозитарії
Journal of Mathematical Physics, Analysis, Geometry| Резюме: | 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 |
|---|