Ondelettes sur l’intervalle. (Wavelets on the interval). (French) Zbl 0753.42015

Meyer, Yves

Rev. Mat. Iberoam. 7, No. 2, 115-133 (1991).

The results concerning the wavelets analysis on the whole real line became classical due to achievements of I. Daubechies, Y. Meyer, S. Mallat and of some other authors. In the present paper the author has solved the difficult problem, how to construct multiresolution analysis of \(L^ 2\)-space and the orthonormal basis of wavelets \(\{\psi_ I\}\), \(I\in J\), on the finite interval \([0,1]\). The results are used for the characterization of the Hölder space \(C^ s[0,1]\) and of the space BMO[0,1]. The Calderón-Zygmund operators on the interval [0,1] are considered.

Reviewer: B.Rubin (Jerusalem)

MSC:

42C40

Nontrigonometric harmonic analysis involving wavelets and other special systems

Keywords:

wavelets; multiresolution analysis; Hölder space; BMO; Calderón- Zygmund operators