On Some Weighted Classes of m-Subharmonic Functions
DOI:
https://doi.org/10.15407/mag20.01.112Ключові слова:
m-субгармонiчна функцiя, ємнiсть, оператор Гессе, збiжнiсть вiдносно m-ємностiАнотація
У цiй роботi ми вивчаємо клас $\mathcal{E}_m(\Omega)$ $m$-субгармонiчних функцiй, введений Лю в [18]. Ми доводимо, що збiжнiсть мiр Гессе виводиться зi збiжностi вiдносно $m$-ємностi для функцiй, що належать $\mathcal{E}_m(\Omega)$ та
задовольняють певнi додатковi умови. Далi ми розповсюджуємо цi результати на клас $\mathcal{E}_{m,\chi}(\Omega)$, який залежить вiд заданої дiйсної функцiї $\chi$. Дано повну характеризацiю цих класiв за допомогою мiри Гессе, а
також теорему пiдпродовження вiдносно $\mathcal{E}_{m,\chi}(\Omega)$.
Mathematical Subject Classification 2020: 32W20, 32U05, 32U15, 32U40
Посилання
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