The Journal of Geometric Analysis

, Volume 11, Issue 2, pp 241–264

Wavelet characterization of weighted spaces

Authors

    • Departamento de Matemáticas, C-XVUniversidad Autónoma de Madrid
  • J. M. Martell
    • Departamento de Matemáticas, C-XVUniversidad Autónoma de Madrid
Article

DOI: 10.1007/BF02921965

Cite this article as:
García-Cuerva, J. & Martell, J.M. J Geom Anal (2001) 11: 241. doi:10.1007/BF02921965

Abstract

We give a characterization of weighted Hardy spaces Hp(w), valid for a rather large collection of wavelets, 0 <p ≤ 1,and weights w in the Muckenhoupt class AWe improve the previously known results and adopt a systematic point of view based upon the theory of vector-valued Calderón-Zygmund operators. Some consequences of this characterization are also given, like the criterion for a wavelet to give an unconditional basis and a criterion for membership into the space from the size of the wavelet coefficients.

Math Subject Classifications

42B2042B2542B3046B15

Key Words and Phrases

waveletsHp spacesAp weightsvector-valued Calderón-Zygmund operatorsLittlewood-Paley theoryunconditional bases

Copyright information

© Mathematica Josephina, Inc. 2001