An atomic decomposition for functions of bounded variation

Daniel Spector; Cody B. Stockdale; Dmitriy Stolyarov

doi:10.1142/S0219199725400024

An atomic decomposition for functions of bounded variation

Daniel Spector^*
, Cody B. Stockdale
, Dmitriy Stolyarov

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we give a decomposition of the gradient measure Du of an arbitrary function of bounded variation u into a linear combination of atoms μ = D_χF, where F is a set of finite perimeter.

Original language	English
Article number	2540002
Journal	Communications in Contemporary Mathematics
DOIs	https://doi.org/10.1142/S0219199725400024
Publication status	Accepted/In press - 2025

Keywords

Bounded variation
Sobolev inequalities
atomic decomposition
dimension estimates

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1142/S0219199725400024

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title = "An atomic decomposition for functions of bounded variation",

abstract = "In this paper, we give a decomposition of the gradient measure Du of an arbitrary function of bounded variation u into a linear combination of atoms μ = DχF, where F is a set of finite perimeter.",

keywords = "Bounded variation, Sobolev inequalities, atomic decomposition, dimension estimates",

author = "Daniel Spector and Stockdale, \{Cody B.\} and Dmitriy Stolyarov",

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AU - Spector, Daniel

AU - Stockdale, Cody B.

AU - Stolyarov, Dmitriy

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AB - In this paper, we give a decomposition of the gradient measure Du of an arbitrary function of bounded variation u into a linear combination of atoms μ = DχF, where F is a set of finite perimeter.

KW - Bounded variation

KW - Sobolev inequalities

KW - atomic decomposition

KW - dimension estimates

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UR - https://www.scopus.com/pages/publications/105019626600#tab=citedBy

U2 - 10.1142/S0219199725400024

DO - 10.1142/S0219199725400024

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SN - 0219-1997

JO - Communications in Contemporary Mathematics

JF - Communications in Contemporary Mathematics

M1 - 2540002

ER -

An atomic decomposition for functions of bounded variation

Abstract

Keywords

ASJC Scopus subject areas

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