In this paper we study approximation problems for functions belonging to 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 , 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.
Cite this article
Laura Angeloni, Approximation Results with Respect to Multidimensional φ-Variation for Nonlinear Integral Operators. Z. Anal. Anwend. 32 (2013), no. 1, pp. 103–128DOI 10.4171/ZAA/1476