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On unconditional polynomial bases inL p and bergman spaces

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In this paper we consider unconditional bases inL p(T), 1<p<∞,p ≠ 2, consisting of trigonometric polynomials. We give a lower bound for the degree of polynomials in such a basis (Theorem 3.4) and show that this estimate is best possible. This is applied to the Littlewood-Paley-type decompositions. We show that such a decomposition has to contain exponential gaps. We also consider unconditional polynomial bases inH p as bases in Bergman-type spaces and show that they provide explicit isomorphisms between Bergman-type spaces and natural sequences spaces.

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Communicated by J. Milne Anderson.

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Wojtaszczyk, P. On unconditional polynomial bases inL p and bergman spaces. Constr. Approx 13, 1–15 (1997). https://doi.org/10.1007/BF02678427

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  • DOI: https://doi.org/10.1007/BF02678427

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