Convergence and rate of approximation in $BV^{\varphi}(\mathbb{R}^N_+)$   for a class of Mellin integral operators
  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. 
Laura Angeloni, Gianluca Vinti
math.FA