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P. Tchamitchian has constructed an atomic decomposition of the real Hardy space    with  L p  -atoms (  ) by rearrangements of wavelet expansion. In this paper, we give a characterization of Triebel–Lizorkin spaces    and Besov spaces    by a BMO family expansion by applying the arguments above.

A characterization of Triebel–Lizorkin spaces and Besov spaces by BMO families expansion