SOME STRONG COMPARISON PRINCIPLES AND CONVERGENCE THEOREMS IN THE CAPACITY AND THE DIRICHLET PROBLEM IN THE CLASS F_p(h)

Le Mau Hai and Tang Van Long

Abstract

           The aim of this paper is to establish the strong comparison principle of Xing type ([Xi1], [Xi2]) for the classes E_p and 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 F_p as well as solve the Dirichlet problem in the class F_p(h).