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 Calderón–Zygmund constants of the frame kernel.