Sharp Bounds for Certain $m$-linear Integral Operators on $p$-adic Function Spaces

Abstract

In this paper, we establish necessary and sufficient conditions for boundedness of $m$-linear $p$-adic integral operators with general homogeneous kernel on $p$-adic Lebesgue spaces and $p$-adic Morrey spaces, respectively. In each case, we obtain the corresponding operator norms. Also, we deal with some particular examples and compare them with the previously known from the literature.