In this paper, we study the regularity of the complex Hessian equation when the right hand has pole singularity. We show the Hölder continuity of the solution to the Dirichlet problem. In particular, for the complex Monge-Ampère equation, we improve a result of [7].

中文翻译：

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一类奇异复数Hessian方程的正则性

本文研究右手具有极点奇点的复数Hessian方程的正则性。我们显示Dirichlet问题的解的Hölder连续性。特别是对于复杂的蒙格-安培方程，我们改进了[7]的结果。