Harmonic analysis of the space BV.

Albert Cohen; Wolfgang Dahmen; Ingrid Daubechies; Ronald DeVore

Revista Matemática Iberoamericana (2003)

  • Volume: 19, Issue: 1, page 235-263
  • ISSN: 0213-2230

Abstract

top
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.

How to cite

top

Cohen, Albert, et al. "Harmonic analysis of the space BV.." Revista Matemática Iberoamericana 19.1 (2003): 235-263. <http://eudml.org/doc/39693>.

@article{Cohen2003,
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 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.},
author = {Cohen, Albert, Dahmen, Wolfgang, Daubechies, Ingrid, DeVore, Ronald},
journal = {Revista Matemática Iberoamericana},
keywords = {Análisis armónico; Espacios de funciones; Funciones de variación acotada; Espacios de Besov; Ondículas; Littlewood-Paley; Interpolación; Espacios normados; bounded variation; wavelet decompositions; weak ; -functionals; interpolation; Gagliardo-Nirenberg inequalities; Besov spaces},
language = {eng},
number = {1},
pages = {235-263},
title = {Harmonic analysis of the space BV.},
url = {http://eudml.org/doc/39693},
volume = {19},
year = {2003},
}

TY - JOUR
AU - Cohen, Albert
AU - Dahmen, Wolfgang
AU - Daubechies, Ingrid
AU - DeVore, Ronald
TI - Harmonic analysis of the space BV.
JO - Revista Matemática Iberoamericana
PY - 2003
VL - 19
IS - 1
SP - 235
EP - 263
AB - 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.
LA - eng
KW - Análisis armónico; Espacios de funciones; Funciones de variación acotada; Espacios de Besov; Ondículas; Littlewood-Paley; Interpolación; Espacios normados; bounded variation; wavelet decompositions; weak ; -functionals; interpolation; Gagliardo-Nirenberg inequalities; Besov spaces
UR - http://eudml.org/doc/39693
ER -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.