Convergence and rate of approximation in $BV^{\varphi}(\mathbb R^N_+)$ for a class of Mellin integral operators

Abstract

In this paper we study convergence results and rate of approximation for a family of linear integral operators of Mellin type in the frame of $BV^{\varphi}(\mathbb R^N_+)$. Here $BV^{\varphi}(\mathbb R^N_+)$ denotes the space of functions with bounded $\varphi-$variation on $\mathbb R^N_+$, defined by means of a concept of multidimensional $\varphi-$variation in the sense of Tonelli.