Convergence and rate of approximation for linear integral operators in BVφ-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 BVφ(RN) (space of functions with bounded φ-variation in RN). Moreover we give a further generalization of the theory introducing the concept of Fφ-variation, where F is a continuous sublinear functional.