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arXiv · 1206.2390

Wavelet frame bijectivity on Lebesgue and Hardy spaces

H. -Q. Bui·R. S. Laugesen
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Abstract

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.

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H. -Q. Bui, R. S. Laugesen. 2012-06-11. Wavelet frame bijectivity on Lebesgue and Hardy spaces. https://arxiv.org/abs/1206.2390

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