Math @ Duke

Publications [#287162] of Ingrid Daubechies
Papers Published
 Cohen, A; Dahmen, W; Daubechies, I; DeVore, R, Harmonic analysis of the space BV,
Revista Matemática Iberoamericana, vol. 19 no. 1
(January, 2003),
pp. 235263, European Mathematical Publishing House [doi]
(last updated on 2019/08/25)
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 weakl1 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 GagliardcNirenbergtype inequalities.


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