Harmonic Analysis of the space BV Academic Article uri icon


  • 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-l1 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 Gagliardc-Nirenberg-type inequalities.

published proceedings

  • Revista Matemtica Iberoamericana

author list (cited authors)

  • Cohen, A., Dahmen, W., Daubechies, I., & DeVore, R.

citation count

  • 66

complete list of authors

  • Cohen, Albert||Dahmen, Wolfgang||Daubechies, Ingrid||DeVore, Ronald

publication date

  • January 2003