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Harmonic analysis of the space BV

Publication ,  Journal Article
Cohen, A; Dahmen, W; Daubechies, I; DeVore, R
Published in: Revista Matematica Iberoamericana
January 1, 2003

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.

Duke Scholars

Published In

Revista Matematica Iberoamericana

DOI

EISSN

2235-0616

ISSN

0213-2230

Publication Date

January 1, 2003

Volume

19

Issue

1

Start / End Page

235 / 263

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 0101 Pure Mathematics
 

Citation

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ICMJE
MLA
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Cohen, A., Dahmen, W., Daubechies, I., & DeVore, R. (2003). Harmonic analysis of the space BV. Revista Matematica Iberoamericana, 19(1), 235–263. https://doi.org/10.4171/RMI/345
Cohen, A., W. Dahmen, I. Daubechies, and R. DeVore. “Harmonic analysis of the space BV.” Revista Matematica Iberoamericana 19, no. 1 (January 1, 2003): 235–63. https://doi.org/10.4171/RMI/345.
Cohen A, Dahmen W, Daubechies I, DeVore R. Harmonic analysis of the space BV. Revista Matematica Iberoamericana. 2003 Jan 1;19(1):235–63.
Cohen, A., et al. “Harmonic analysis of the space BV.” Revista Matematica Iberoamericana, vol. 19, no. 1, Jan. 2003, pp. 235–63. Scopus, doi:10.4171/RMI/345.
Cohen A, Dahmen W, Daubechies I, DeVore R. Harmonic analysis of the space BV. Revista Matematica Iberoamericana. 2003 Jan 1;19(1):235–263.

Published In

Revista Matematica Iberoamericana

DOI

EISSN

2235-0616

ISSN

0213-2230

Publication Date

January 1, 2003

Volume

19

Issue

1

Start / End Page

235 / 263

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 0101 Pure Mathematics