On metric semigroups-valued functions of bounded Riesz-Φ-variation in several variables

Using classical techniques related to the so-called Hardy–Vitali variation, we present the class of X -valued functions of bounded Φ -variation in several variables, where ( X , d , + ) is a metric semigroup. We exhibit some of the main properties of this class; among them, we show that this class c...

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Bibliographic Details
Published in:Boletín de la Sociedad Matemática Mexicana 2018-04, Vol.24 (1), p.133-153
Main Authors: Bracamonte, M., Ereú, J., Giménez, J., Merentes, N.
Format: Article
Language:English
Subjects:
Mathematical analysis
Mathematics
Mathematics and Statistics
Original Article
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Summary:Using classical techniques related to the so-called Hardy–Vitali variation, we present the class of X -valued functions of bounded Φ -variation in several variables, where ( X , d , + ) is a metric semigroup. We exhibit some of the main properties of this class; among them, we show that this class can be made into a normed space and present a counterpart of the renowned Riesz’s Lemma for the case in which X = R with its usual metric.
ISSN:1405-213X
2296-4495
DOI:10.1007/s40590-016-0138-2