Some finite weighted energy classes of m-subharmonic functions

Abstract

Let [Formula: see text] be a bounded [Formula: see text]-hyperconvex domain ([Formula: see text]) and [Formula: see text] be a weighted function. In this paper, we first prove a characterization of the finite weighted energy class [Formula: see text] and give an upper-bound for [Formula: see text]-capacity in the class [Formula: see text]. Then, by using these estimates, we construct some classes of finite weighted energy functions in [Formula: see text]-subharmonic functions class and give some corollaries about the relationship between these finite weighted energy functions classes.