Abstract
Using classical techniques related to the so-called Hardy–Vitali variation, we present the class of X-valued functions of bounded \(\Phi \)-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 \(X=\mathbb {R}\) with its usual metric.
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The authors would like to thank the referee of the first version of this paper for his/her valuable comments and suggestions.
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This research has been partly supported by the Central Bank of Venezuela.
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Bracamonte, M., Ereú, J., Giménez, J. et al. On metric semigroups-valued functions of bounded Riesz-\(\Phi \)-variation in several variables. Bol. Soc. Mat. Mex. 24, 133–153 (2018). https://doi.org/10.1007/s40590-016-0138-2
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DOI: https://doi.org/10.1007/s40590-016-0138-2