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
APA
Chicago
ICMJE
MLA
NLM
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