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 phi-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 phi(R-N) (space of functions with bounded phi-variation in R-N). Moreover we give a further generalization of the theory introducing the concept of F-phi-variation, where F is a continuous sublinear functional. (c) 2008 Elsevier Inc. All rights reserved.