Rate of approximation for multivariate sampling Kantorovich operators on some functions spaces

Abstract

In this paper, the problem of the order of approximation for the multivariate sampling Kantorovich operators is studied. The cases of uniform approximation for uniformly continuous and bounded functions/signals belonging to Lipschitz classes and the case of the modular approximation for functions in Orlicz spaces are considered. In the latter context, Lipschitz classes of Zygmund-type which take into account of the modular functional involved are introduced. Applications to $L^p(\R^n)$, interpolation and exponential spaces can be deduced from the general theory formulated in the setting of Orlicz spaces. The special cases of multivariate sampling Kantorovich operators based on kernels of the product type and constructed by means of Fej\'er's and B-spline kernels have been studied in details.