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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Subsequences of the Haar basis consisting of full levels in $ H_p$ for $ 0 < p < \infty$


Author: K. Smela
Journal: Proc. Amer. Math. Soc. 135 (2007), 1709-1716
MSC (2000): Primary 43A17, 42C20
Published electronically: November 14, 2006
MathSciNet review: 2286080
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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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Additional Information

K. Smela
Affiliation: Department of Mathematics, Rzeszow University of Technology, 35-959 Rzeszow, ul. W. Pola 2, Poland
Email: smelakrz@prz.rzeszow.pl

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08616-3
PII: S 0002-9939(06)08616-3
Received by editor(s): May 9, 2005
Received by editor(s) in revised form: December 21, 2005
Published electronically: November 14, 2006
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2006 American Mathematical Society