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Rendiconti Lincei - Matematica e Applicazioni


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Volume 25, Issue 3, 2014, pp. 217–232
DOI: 10.4171/RLM/675

Published online: 2014-08-31

Convergence and rate of approximation in $BV^{\varphi}(\mathbb R^N_+)$ for a class of Mellin integral operators

Laura Angeloni[1] and Gianluca Vinti[2]

(1) Università degli Studi di Perugia, Italy
(2) Università degli Studi di Perugia, Italy

In this paper we study convergence results and rate of approximation for a family of linear integral operators of Mellin type in the frame of $BV^{\varphi}(\mathbb R^N_+)$. Here $BV^{\varphi}(\mathbb R^N_+)$ denotes the space of functions with bounded $\varphi-$variation on $\mathbb R^N_+$, defined by means of a concept of multidimensional $\varphi-$variation in the sense of Tonelli.

Keywords: Mellin integral operators, multidimensional $\varphi-$variation, rate of approximation, Lipschitz classes, $\varphi-$modulus of smoothness

Angeloni Laura, Vinti Gianluca: Convergence and rate of approximation in $BV^{\varphi}(\mathbb R^N_+)$ for a class of Mellin integral operators. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 25 (2014), 217-232. doi: 10.4171/RLM/675