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

  • 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
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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Published
20.06.2023
How to Cite
ZawayM., and HbilJ. “Complex Hessian-Type Equations in the Weighted $m$-Subharmonic Class”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 75, no. 6, June 2023, pp. 805 -16, doi:10.37863/umzh.v75i6.7122.
Section
Research articles