A pointwise characterization of functions of bounded variation on metric spaces
type: Item
instance of: scholarly article
title: A pointwise characterization of functions of bounded variation on metric spaces
zbMATH Open document ID: 1327.46036
author: Panu Lahti
author: Heli Tuominen
published in: Ricerche di Matematica
publication date: 2014-12-08T00:00:00Z
full work available at URL: https://arxiv.org/abs/1301.6897
review text: This paper gives a characterization of the space of functions of bounded variation in terms of a pointwise inequality connected to the maximal function of a measure. The result hold in doubling metric measure spaces supporting a 1-Poincaré inequality. In this setting, functions of bounded variation can be defined via total variation \[ \|Du\|(X)=\inf\left\{\liminf_{i\rightarrow\infty} \int_{X}\text{Lip}\, u_{i}\,d\mu\,:\, u_{i}\in \text{Lip}_{loc}(X),u_{i}\rightarrow u\text{ in } L^{1}_{loc}(X)\right\}, \] where \(\text{Lip}\, u\) is a local Lipschitz constant of \(u\).
reviewed by: Riikka Korte
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 26B30
Mathematics Subject Classification ID: 28A12
zbMATH DE Number: 6378255
zbMATH Keywords: function of bounded variation
zbMATH Keywords: metric measure space
zbMATH Keywords: pointwise characterization
zbMATH Keywords: doubling measure
MaRDI profile type: Publication
OpenAlex ID: W3106476464
Wikidata QID: Q109992632
arXiv ID: 1301.6897
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DOI: 10.1007/S11587-013-0161-9
description: scientific article