Subsequences of the Haar basis consisting of full levels in 𝐻_{𝑝} for 0<𝑝<∞

Smela, K.

doi:10.1090/S0002-9939-06-08616-3

Subsequences of the Haar basis consisting of full levels in $H_p$ for $0 < p < \infty$
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Proc. Amer. Math. Soc. 135 (2007), 1709-1716 Request permission

Abstract:

We find a condition to be satisfied by strictly increasing sequences of natural numbers guaranteeing that corresponding subsequences of the Haar basis (consisting of full levels) are equivalent or span isomorphic spaces. This applies in particular to Hardy spaces for $0 < p < \infty$. We also construct a continuum of greedy nonequivalent bases in $H_p$.

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