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Zeitschrift für Analysis und ihre Anwendungen


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Volume 32, Issue 1, 2013, pp. 103–128
DOI: 10.4171/ZAA/1476

Published online: 2013-01-27

Approximation Results with Respect to Multidimensional φ-Variation for Nonlinear Integral Operators

Laura Angeloni[1]

(1) Università degli Studi di Perugia, Italy

In this paper we study approximation problems for functions belonging to $BV$ φ-spaces (spaces of functions of bounded φ-variation) in multidimensional setting. In particular, using a multidimensional concept of φ-variation in the sense of Tonelli introduced in [4], we obtain estimates, convergence results and, by means of suitable Lipschitz classes, results about the order of approximation for a family of nonlinear convolution integral operators.

Keywords: Nonlinear convolution integral operators, multidimensional φ-variation, rate of approximation, Lipschitz classes, φ-modulus of smoothness

Angeloni Laura: Approximation Results with Respect to Multidimensional φ-Variation for Nonlinear Integral Operators. Z. Anal. Anwend. 32 (2013), 103-128. doi: 10.4171/ZAA/1476