Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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$.

References [Enhancements On Off] (What's this?)

  • 1. J.L. Gamlen, R. J. Gaudet, On subsequences of the Haar system in $ L^p$ $ (1 < p < \infty)$, Israel J. Math. 15 (1973), 404-413. MR 0328575 (48:6917)
  • 2. N.J. Kalton, N.T. Peck, J.W. Roberts, An F-Space Sampler, London Math. Soc. Lecture Notes 89, Cambridge University Press 1984, Cambridge.MR 0808777 (87c:46002)
  • 3. S.V. Konyagin, V.N. Temlyakov, A remark on greedy approximation in Banach spaces, East J. Approx. 5 (1999), 365-379. MR 1716087 (2000j:46020)
  • 4. J. Lindenstrauss, L. Tzafriri, Classical Banach Spaces I, Springer-Verlag 1977, Berlin. MR 0500056 (58:17766)
  • 5. P.F.X. Müller, On subsequences of the Haar basis in $ H^1(\delta)$ and isomorphism between $ H^1$-spaces, Studia Math. 85 (1987), 73-90. MR 0879418 (88h:46043)
  • 6. P. Wojtaszczyk, Banach Spaces for Analysts, Cambridge Studies in Advanced Math. vol. 25, Cambridge University Press 1991, Cambridge. MR 1144277 (93d:46001)
  • 7. P. Wojtaszczyk, Uniqueness of unconditional bases in quasi-Banach spaces with applications to Hardy spaces, II, Israel J. Math. 97 (1997), 253-280.MR 1441252 (98g:46007)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 43A17, 42C20

Retrieve articles in all journals with MSC (2000): 43A17, 42C20

Additional Information

K. Smela
Affiliation: Department of Mathematics, Rzeszow University of Technology, 35-959 Rzeszow, ul. W. Pola 2, Poland

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

American Mathematical Society