Harmonic analysis of the space BV

Journal Article (Journal Article)

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.

Full Text

Duke Authors

Cited Authors

  • Cohen, A; Dahmen, W; Daubechies, I; DeVore, R

Published Date

  • January 1, 2003

Published In

Volume / Issue

  • 19 / 1

Start / End Page

  • 235 - 263

International Standard Serial Number (ISSN)

  • 0213-2230

Digital Object Identifier (DOI)

  • 10.4171/RMI/345

Citation Source

  • Scopus