# A New Concept of Multidimensional Variation in the Sense of Riesz and Applications to Integral Operators

A New Concept of Multidimensional Variation in the Sense of Riesz and Applications to Integral... In this paper, we introduce and study a new multidimensional generalization in the sense of Tonelli of the Riesz–Medvedev $$\varphi$$ 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 $$\varphi$$ φ -variation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mediterranean Journal of Mathematics Springer Journals

# A New Concept of Multidimensional Variation in the Sense of Riesz and Applications to Integral Operators

, Volume 14 (4) – Jun 13, 2017
21 pages

/lp/springer_journal/a-new-concept-of-multidimensional-variation-in-the-sense-of-riesz-and-qqod8Rc7Jz
Publisher
Springer International Publishing
Subject
Mathematics; Mathematics, general
ISSN
1660-5446
eISSN
1660-5454
D.O.I.
10.1007/s00009-017-0947-1
Publisher site
See Article on Publisher Site

### Abstract

In this paper, we introduce and study a new multidimensional generalization in the sense of Tonelli of the Riesz–Medvedev $$\varphi$$ 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 $$\varphi$$ φ -variation.

### Journal

Mediterranean Journal of MathematicsSpringer Journals

Published: Jun 13, 2017

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