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

Keywords: m-subharmonic function, Capacity, Hessian operator.

Abstract

UDC 517.5

We study the existence of a solution to a general type of complex Hessian equation on some Cegrell classes. For a given measure $\mu$ defined on an $m$-hyperconvex domain $\Omega \subset \mathbb{C}^n,$ under suitable conditions, we prove that the equation $\chi(.) H_m(.)=\mu$ has a solution that belongs to the class $\mathcal{E}_{m,\chi}(\Omega).$

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