TITLE:
On Second Riesz Φ-Variation of Normed Space Valued Maps
AUTHORS:
Mireya Bracamonte, José Giménez, N. Merentes, J. L. Sánchez
KEYWORDS:
Young Function; Φ-Variation; Second Φ-Variation of a Function
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.2 No.1,
January
6,
2012
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.