Approximation Results with Respect to Multidimensional φ-Variation for Nonlinear Integral Operators

In this paper we study approximation problems for functions belonging to BV phi-spaces (spaces of functions of bounded phi-variation) in multidimensional setting. In particular, using a multidimensional concept of phi-variation in the sense of Tonelli introduced in [4], we obtain estimates, convergence results and, by means of suitable Lipschitz classes, results about the order of approximation for a family of nonlinear convolution integral operators.