Harmonic Analysis of the space BV
Cohen, Albert ; Dahmen, Wolfgang ; Daubechies, Ingrid ; DeVore, Ronald
Rev. Mat. Iberoamericana, Tome 19 (2003) no. 2, p. 235-263 / Harvested from Project Euclid
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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-$\ell^1$ 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.
Publié le : 2003-03-15
Classification:  Bounded variation,  wavelet decompositions,  weak $\ell_1$,  K-functionals,  interpolation,  Gagliardo-Nirenberg inequalities,  Besov spaces,  42C40,  46B70,  26B35,  42B25 
@article{1049123087,
     author = {Cohen, Albert and Dahmen, Wolfgang and Daubechies, Ingrid and DeVore, Ronald},
     title = {Harmonic Analysis of the space BV},
     journal = {Rev. Mat. Iberoamericana},
     volume = {19},
     number = {2},
     year = {2003},
     pages = { 235-263},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1049123087}
}

Cohen, Albert; Dahmen, Wolfgang; Daubechies, Ingrid; DeVore, Ronald. Harmonic Analysis of the space BV. Rev. Mat. Iberoamericana, Tome 19 (2003) no. 2, pp.  235-263. http://gdmltest.u-ga.fr/item/1049123087/