Wavelet Frame Bijectivity on Lebesgue and Hardy Spaces

H. Q. Bui, R. S. Laugesen

Research output: Contribution to journalArticle

Abstract

We prove a sufficient condition for frame-type wavelet series in Lp, 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 languageEnglish (US)
Pages (from-to)376-409
Number of pages34
JournalJournal of Fourier Analysis and Applications
Volume19
Issue number2
DOIs
StatePublished - Mar 18 2013

Keywords

  • Calderón-Zygmund operator
  • Mexican hat

ASJC Scopus subject areas

  • Analysis
  • Mathematics(all)
  • Applied Mathematics

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