Convergence for $m-$positive currents and $m-$subharmonic functions

Abstract

In this paper we  give sufficient conditions on $m-$subharmonic functions $f_k$ and $m-$positive currents $R_k$ of bidegree $(p,p)$ to ensure the convergence of $f_k.R_k\wedge\gamma^{m-p}$ in the sense of currents. As application of this result, we treat the special case $R_k= (dd^cf_k)^p$ and we show that one of the condition  of the main result is necessary in this case.