On Second Riesz Φ-Variation of Normed Space Valued Maps

Mireya Bracamonte, José Giménez, N. Merentes, J. L. Sánchez

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DOI: 10.4236/apm.2012.21011                

Abstract

In this article we present a Riesz-type generalization of the concept of second variation of normed space valued functions defined on an interval [a,b]R. We show that a function f ^[a,b], where X is a reflexive Banach space, is of bounded second Φ-variation, in the sense of Riesz, if and only if it can be expressed as the (Bochner) integral of a function of bounded (first) $\Phi$-variation. We provide also a Riesz lemma type inequality to estimate the total second Riesz-Φ-variation introduced.

Keywords

Young Function; Φ-Variation; Second Φ-Variation of a Function

Conflicts of Interest

The authors declare no conflicts of interest.

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