Convergence and rate of approximation for linear integral operators in BV^φ-spaces in multidimensional setting

In this paper, where for the first time it is introduced a multidimensional concept of φ-variation in the sense of Tonelli, we extend previous results concerning convergence, order of approximation and higher order of approximation for linear integral operators in BV^φ(R^N) (space of functions with bounded φ-variation in R^N). Moreover we give a further generalization of the theory introducing the concept of F^φ-variation, where F is a continuous sublinear functional.