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Zeitschrift für Analysis und ihre Anwendungen


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Volume 34, Issue 3, 2015, pp. 343–356
DOI: 10.4171/ZAA/1543

Published online: 2015-07-08

A Characterization of Absolute Continuity by means 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 the case of classical convolution operators, an important characterization of absolute continuity is given in terms of convergence in variation. In this paper we will study this problem for Mellin integral operators, proving analogous characterizations in the frame of the classical $BV$-spaces, both in the one-dimensional and in the multidimensional setting.

Keywords: Mellin integral operators, absolute continuity, multidimensional variation, convergence in variation

Angeloni Laura, Vinti Gianluca: A Characterization of Absolute Continuity by means of Mellin Integral Operators. Z. Anal. Anwend. 34 (2015), 343-356. doi: 10.4171/ZAA/1543