Abstract
We prove that a wide class of quasi-Banach spaces has a unique up to a permutation unconditional basis. This applies in particular to Hardy spacesH p forp<1. We also investigate the structure of complemented subspaces ofH p (D). The proofs use in essential way matching theory.
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This research was supported in part by KBN grant N. 2P301004.06 and by the Overseas Visiting Scholarship of St. John’s College, Cambridge.
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Wojtaszczyk, P. Uniqueness of unconditional bases in quasi-banach spaces with applications to hardy spaces, II. Isr. J. Math. 97, 253–280 (1997). https://doi.org/10.1007/BF02774040
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DOI: https://doi.org/10.1007/BF02774040