Acta Mathematica Vietnamica
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SOME STRONG COMPARISON PRINCIPLES AND CONVERGENCE THEOREMS IN THE CAPACITY AND THE DIRICHLET PROBLEM IN THE CLASS $\mathcal F_p(h)$
LE MAU HAI, TANG VAN LONG
Abstract
The aim of this paper is to establish the strong comparison principle of Xing type ([Xi1], [Xi2]) for the classes $\mathcal E_p$ and $\mathcal F_p$. As an application of the obtained results, we investigate the convergence in the capacity of the complex Monge-Ampère operator for the class $\mathcal F_p$ as well as solve the Dirichlet problem in the class $\mathcal F_p(h)$.