A characterization of absolute continuity by means of Mellin integral operators
type: Item
instance of: scholarly article
title: A characterization of absolute continuity by means of Mellin integral operators
zbMATH Open document ID: 1323.26014
DOI: 10.4171/ZAA/1543
author: Laura Angeloni
author: Gianluca Vinti
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2015-09-22T00:00:00Z
review text: Summary: 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 \(\mathrm{BV}\)-spaces, both in the one-dimensional and in the multidimensional setting.
Mathematics Subject Classification ID: 26A46
Mathematics Subject Classification ID: 26A45
Mathematics Subject Classification ID: 26B30
Mathematics Subject Classification ID: 47G10
zbMATH DE Number: 6484446
zbMATH Keywords: Mellin integral operators
zbMATH Keywords: absolute continuity
zbMATH Keywords: multidimensional variation
zbMATH Keywords: convergence in variation
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6484446