Open Access
March, 2003 Harmonic Analysis of the space BV
Albert Cohen, Wolfgang Dahmen, Ingrid Daubechies, Ronald DeVore
Rev. Mat. Iberoamericana 19(1): 235-263 (March, 2003).


We establish new results on the space BV of functions with bounded variation. While it is well known that this space admits no unconditional basis, we show that it is "almost" characterized by wavelet expansions in the following sense: if a function $f$ is in BV, its coefficient sequence in a BV normalized wavelet basis satisfies a class of weak-$\ell^1$ type estimates. These weak estimates can be employed to prove many interesting results. We use them to identify the interpolation spaces between BV and Sobolev or Besov spaces, and to derive new Gagliardo-Nirenberg-type inequalities.


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Albert Cohen. Wolfgang Dahmen. Ingrid Daubechies. Ronald DeVore. "Harmonic Analysis of the space BV." Rev. Mat. Iberoamericana 19 (1) 235 - 263, March, 2003.


Published: March, 2003
First available in Project Euclid: 31 March 2003

zbMATH: 1044.42028
MathSciNet: MR1993422

Primary: 26B35 , 42B25 , ‎42C40 , 46B70

Keywords: Besov spaces , Bounded variation , Gagliardo-Nirenberg inequalities , interpolation , K-functionals , wavelet decompositions , weak $\ell_1$

Rights: Copyright © 2003 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.19 • No. 1 • March, 2003
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