$(m, \psi, \delta)-$capacity and its properties

Abstract

In this paper, we introduce the concept of the generalized $(m, \psi, \delta)-$capacity in the complex space $\mathbb{C}^n$, within the class of $m-$subharmonic functions. We give a relation between $(m, \psi, \delta)-$capacity and $(m, \psi, \delta)-$subharmonic measure. Moreover, we prove that the capacity vanishes on $m-$polar sets and vice versa.