Unconditional basic sequence in $L^p(\mu )$ and its $l^p$-stability
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- by Lihua Yang PDF
- Proc. Amer. Math. Soc. 127 (1999), 455-464 Request permission
Abstract:
This paper is concerned with unconditional basic sequences in $L^p(\mu )$. We prove that, under some conditions, a sequence in $L^p(\mu )$ is a bounded unconditional basic sequence if and only if it is $l^p$-stable. At last the results are applied to the shift-invariant basic sequences generated by a finite subset of $L^p(R^s)$, which is very important in wavelet analysis.References
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Additional Information
- Lihua Yang
- Affiliation: Department of Scientific Computing and Computer Applications, Zhongshan University, 510275, People’s Republic of China; Institute of Mathematics, Academy Sinica, Beijing, 100080, People’s Republic of China
- Email: yang@comp.hkbu.edu.hk, ylh@math03.math.ac.cn
- Received by editor(s): October 14, 1996
- Received by editor(s) in revised form: May 21, 1997
- Communicated by: J. Marshall Ash
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 455-464
- MSC (1991): Primary 46B20
- DOI: https://doi.org/10.1090/S0002-9939-99-04638-9
- MathSciNet review: 1473673