Complex Hessian-type equations in the weighted $m$-subharmonic class

Mohamed  Zaway; Jawhar  Hbil

doi:10.37863/umzh.v75i6.7122

Mohamed Zaway Department of Mathematics, Faculty of Sciences of Sfax, University of Sfax, Tunisia and Irescomath Laboratory, Gabes University, Zrig Gabes, Tunisia
Jawhar Hbil Department of Mathematics, Jouf University, Sakaka, Saudi Arabia and Irescomath Laboratory, Gabes University, Zrig Gabes, Tunisia

DOI: https://doi.org/10.37863/umzh.v75i6.7122

Анотація

УДК 517.5

Комплексні рівняння типу Гессе у зваженому $m$-субгармонічному класі

Досліджено існування розв’язку для комплексного рівняння Гессе загального типу на деяких класах Сегрелля. Для заданої міри $\mu$, що визначена на $m$-гіперопуклій області $\Omega \subset \mathbb{C}^n,$ доведено, що за відповідних умов рівняння $\chi(.) H_m(.)= \mu$ має розв’язок, який належить класу $\mathcal{E}_{m,\chi}(\Omega).$

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