A Review on Approximation Results for Integral Operators in the Space of Functions of Bounded Variation. (26th September 2016)

• Record Type: Journal Article
• Authors: Angeloni, Laura; Vinti, Gianluca
• Other Names: Hudzik Henryk Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2016(2016)
• Publication Date: 2016-09-26
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2016/3843921
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : We present a review on recent approximation results in the space of functions of bounded variation for some classes of integral operators in the multidimensional setting. In particular, we present estimates and convergence in variation results for both convolution and Mellin integral operators with respect to the Tonelli variation. Results with respect to a multidimensional concept of φ -variation in the sense of Tonelli are also presented.