Wavelet Frame Bijectivity on Lebesgue and Hardy Spaces

H. Q. Bui; R. S. Laugesen

doi:10.1007/s00041-013-9268-3

Wavelet Frame Bijectivity on Lebesgue and Hardy Spaces

H. Q. Bui, R. S. Laugesen

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We prove a sufficient condition for frame-type wavelet series in L^p, the Hardy space H¹, 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.

Original language	English (US)
Pages (from-to)	376-409
Number of pages	34
Journal	Journal of Fourier Analysis and Applications
Volume	19
Issue number	2
DOIs	https://doi.org/10.1007/s00041-013-9268-3
State	Published - Mar 18 2013

Keywords

Calderón-Zygmund operator
Mexican hat

ASJC Scopus subject areas

Analysis
Mathematics(all)
Applied Mathematics

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10.1007/s00041-013-9268-3

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Wavelet Frame Bijectivity on Lebesgue and Hardy Spaces

Abstract

Keywords

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