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