JournalsrmiVol. 19, No. 1pp. 235–263

Harmonic Analysis of the space BV

  • Albert Cohen

    Université Pierre et Marie Curie, Paris, France
  • Wolfgang Dahmen

    Technische Hochschule Aachen, Germany
  • Ingrid Daubechies

    Duke University, Durham, USA
  • Ronald A. DeVore

    Texas A&M University, College Station, USA
Harmonic Analysis of the space BV cover
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Abstract

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 ff is in BV, its coefficient sequence in a BV normalized wavelet basis satisfies a class of weak-1\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.

Cite this article

Albert Cohen, Wolfgang Dahmen, Ingrid Daubechies, Ronald A. DeVore, Harmonic Analysis of the space BV. Rev. Mat. Iberoam. 19 (2003), no. 1, pp. 235–263

DOI 10.4171/RMI/345