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In this paper, the problem of the order of approximation for the multivariatesampling Kantorovich operators is studied. The cases of the uniformapproximation for uniformly continuous and bounded functions/signals belongingto Lipschitz classes and the case of the modular approximation for functions inOrlicz spaces are considered. In the latter context, Lipschitz classes ofZygmund-type which take into account of the modular functional involved areintroduced. Applications to Lp(R^n), interpolation and exponential spaces canbe deduced from the general theory formulated in the setting of Orlicz spaces.The special cases of multivariate sampling Kantorovich operators based onkernels of the product type and constructed by means of Fejer's and B-splinekernels have been studied in details.

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