Absolute continuity for Banach space valued mappings
type: Item
instance of: scholarly article
title: Absolute continuity for Banach space valued mappings
zbMATH Open document ID: 1150.26008
DOI: 10.1007/BF03031433
author: Calogero Vetro
author: Cristina Di Bari
publication date: 2007-08-07T00:00:00Z
review text: The authors generalize the concept of variation, namely \(p,\lambda,\delta\)-variation, of Banach-space valued functions defined in an open set of \(\mathbb R^n\), by means of gage-fine partitions. The idea of considering gage-fine partitions for defining the variation of a function is not new. In a previous paper by the same authors [J. Math. Anal. Appl. 299, No. 1, 227--234 (2004; Zbl 1124.26009)], a variation-type concept using gage-fine partitions is considered for real valued functions. In the present paper, the authors characterize the class of functions of bounded \(p,\lambda,\delta\)-variation (Theorems 5 and 6) and prove that bounded \(p,\lambda,\delta\)-variation implies Frechét differentiability almost everywhere. They also specialize some results for \(p,\lambda,\delta\)-absolute continuous functions.
reviewed by: M. Federson
Mathematics Subject Classification ID: 26B30
zbMATH DE Number: 5177438
MaRDI profile type: Publication
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published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 5177438