Harmonic analysis of the space BV

Autores: Wolfgang Dahmen, Ronald DeVore, Albert Cohen , Ingrid Daubechies
Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 19, Nº 1, 2003, págs. 235-263
Idioma: inglés
DOI: 10.4171/rmi/345
Títulos paralelos:
- Análisis armónico del espacio BV.
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Resumen
- 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 Gagliardo-Nirenberg-type inequalities