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A New Concept of Multidimensional Variation in the Sense of Riesz and Applications to Integral Operators
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A New Concept of Multidimensional Variation in the Sense of Riesz and Applications to Integral Operators
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Journal Article
A New Concept of Multidimensional Variation in the Sense of Riesz and Applications to Integral Operators
2017
Overview
In this paper, we introduce and study a new multidimensional generalization in the sense of Tonelli of the Riesz–Medvedev
φ
-variation, proving in particular a multidimensional generalization of the Riesz–Medvedev theorem. We finally discuss an application of such concept of variation to some approximation problems: in particular, we obtain some estimates and convergence results by means of convolution integral operators in the space of functions of bounded
φ
-variation.
Publisher
Springer International Publishing,Springer Nature B.V
