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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Wavelet bases in rearrangement
invariant function spaces


Author: Paolo M. Soardi
Journal: Proc. Amer. Math. Soc. 125 (1997), 3669-3673
MSC (1991): Primary 42C15
DOI: https://doi.org/10.1090/S0002-9939-97-04207-X
MathSciNet review: 1443168
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Abstract: We point out that the well known characterization of $L^{p}$ spaces ($1<p<\infty $) in terms of orthogonal wavelet bases extends to any separable rearrangement invariant Banach function space $X$ on $R^{n}$ (equipped with Lebesgue measure) with nontrivial Boyd's indices. Moreover we show that such bases are unconditional bases of $X$.


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Additional Information

Paolo M. Soardi
Email: soardi@vmimat.mat.unimi.it

DOI: https://doi.org/10.1090/S0002-9939-97-04207-X
Received by editor(s): July 17, 1996
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1997 American Mathematical Society