Wavelet frame bijectivity on Lebesgue and Hardy spaces
  We prove a sufficient condition for frame-type wavelet series in $L^p$, the Hardy space $H^1$, 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. 
H.-Q. Bui and R. S. Laugesen
math.CA