Wavelet frame bijectivity on Lebesgue and Hardy spaces
Classical Analysis and ODEs
2012-06-13 v1
Abstract
We prove a sufficient condition for frame-type wavelet series in , the Hardy space , and BMO. For example, functions in these spaces are shown to have expansions in terms of the Mexican hat wavelet, thus giving a strong answer to an old question of Meyer. Bijectivity of the wavelet frame operator acting on Hardy space is established with the help of new frequency-domain estimates on the Calder\'on-Zygmund constants of the frame kernel.
Keywords
Cite
@article{arxiv.1206.2390,
title = {Wavelet frame bijectivity on Lebesgue and Hardy spaces},
author = {H. -Q. Bui and R. S. Laugesen},
journal= {arXiv preprint arXiv:1206.2390},
year = {2012}
}
Comments
23 pages, 7 figures