# 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

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topCohen, 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 -

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