English

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 LpL^p, the Hardy space H1H^1, 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

R2 v1 2026-06-21T21:17:43.574Z