Nonlinear multivariate sampling Kantorovich operators: quantitative estimates in functional spaces

In real world applications, signals can be suitably reconstructed by nonlinear procedures; this justifies the study of nonlinear approximation operators. In this paper, we prove some quantitative estimates for the nonlinear sampling Kantorovich operators in the multivariate setting using the modulus of smoothness of $L^p(\mathbb{R}^n)$. The above results have been then extended to the general case of Orlicz spaces $L^{\varphi}(\mathbb{R}^n)$, so obtaining quantitative estimates in several instances of well-known and useful spaces.