Approximation results by multivariate sampling Kantorovich series in Musielak-Orlicz spaces

In this paper we study the theory of the so-called multivariate sampling Kantorovich operators in the general frame of the Musielak-Orlicz spaces. The main result in this context is a modular convergence theorem, that can be proved by density arguments. Several concrete cases of Musielak-Orlicz spaces and of kernel functions are presented and discussed.