Open Access
2004-2005 On the dual space of BV-integrable functions in Euclidean space
Lee Tuo-Yeong
Real Anal. Exchange 30(1): 323-328 (2004-2005).


The dual space (with respect to the Alexiewicz norm) of the class of ${\cal BV}$-integrable functions on a compact cell ${\mathop{\prod}\limits_{i=1}^{m}} [a_i, b_i] \subset {\mathbb R}^m$ is shown to be isometrically isomorphic to the space of finite signed Borel measures on ${\mathop{\prod}\limits_{i=1}^{m}} [a_i, b_i)$, and the usual integral representation theorem holds. An example is also given to show that Lipschitz functions are not part of this dual space. This answers a question of Thierry De Pauw.


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Lee Tuo-Yeong. "On the dual space of BV-integrable functions in Euclidean space." Real Anal. Exchange 30 (1) 323 - 328, 2004-2005.


Published: 2004-2005
First available in Project Euclid: 27 July 2005

zbMATH: 1080.26007
MathSciNet: MR2127537

Primary: ‎46E99
Secondary: 26E99

Keywords: BV-integral , Finite signed Borel measure

Rights: Copyright © 2004 Michigan State University Press

Vol.30 • No. 1 • 2004-2005
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