Multivariate sampling Kantorovich operators: quantitative estimates in Orlicz spaces

Abstract

In this paper, we establish a quantitative estimate for multivariate sampling Kantorovich operators by means of the modulus of smoothness in the general setting of Orlicz spaces. As a consequence, the qualitative order of convergence can be obtained, in case of functions belonging to suitable Lipschitz classes. In the particular instance of Lp-spaces, using a direct approach, we obtain a sharper estimate than that one that can be deduced from the general case