## Journal of Integral Equations and Applications

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

#### Abstract

In this paper, the problem of the order of approximation for the multivariate sampling Kantorovich operators is studied. The cases of 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 $L^p(\R^n)$, 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 Fej\'er's and B-spline kernels have been studied in details.

#### Article information

Source
J. Integral Equations Applications, Volume 26, Number 4 (2014), 455-481.

Dates
First available in Project Euclid: 9 January 2015

https://projecteuclid.org/euclid.jiea/1420812881

Digital Object Identifier
doi:10.1216/JIE-2014-26-4-455

Mathematical Reviews number (MathSciNet)
MR3299827

Zentralblatt MATH identifier
1308.41017

#### Citation

Costarelli, Danilo; Vinti, Gianluca. Rate of approximation for multivariate sampling Kantorovich operators on some functions spaces. J. Integral Equations Applications 26 (2014), no. 4, 455--481. doi:10.1216/JIE-2014-26-4-455. https://projecteuclid.org/euclid.jiea/1420812881

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