Convergence and rate of approximation for linear integral operators in -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.