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

Abstract

In this paper we study approximation problems for functions belonging to $BV$ φ-spaces (spaces of functions of bounded φ-variation) in multidimensional setting. In particular, using a multidimensional concept of φ-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.