  In this paper, the problem of the order of approximation for the multivariate
sampling Kantorovich operators is studied. The cases of the 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 Lp(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 Fejer's and B-spline
kernels have been studied in details.
