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Characterization of BMO in terms of rearrangement-invariant Banach function spaces. (English) Zbl 1174.42025

Summary: The atomic decomposition of Hardy spaces by atoms defined by rearrangement-invariant Banach function spaces is proved in this paper. Using this decomposition, we obtain the characterizations of BMO and Lipschitz spaces by rearrangement-invariant Banach function spaces. We also provide the sharp function characterization of the rearrangement-invariant Banach function spaces.

MSC:

42B30 \(H^p\)-spaces
42B35 Function spaces arising in harmonic analysis
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