Approximation results with respect to multidimensional \(\varphi \)-variation for nonlinear integral operators
Summary: We study approximation problems for functions belonging to \(BV\varphi \)-spaces (spaces of functions of bounded \(\varphi \)-variation) in a multidimensional setting. In particular, using a multidimensional concept of \(\varphi \)-variation in the sense of Tonelli introduced in [the author and \textit{G. Vinti}, J. Math. Anal. Appl. 349, No. 2, 317--334 (2009; Zbl 1154.26017)], 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.
nonlinear convolution integral operators
scientific article; zbMATH DE number 6143108
scientific article