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

Abstract:

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.

Año de publicación:

2018

Keywords:

• Riesz’s Lemma
• Φ -Variation
• Metric semigroup
• φ-function

Fuente:

scopus

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