A remarkable rearrangement of the Haar system in $L_p$
HTML articles powered by AMS MathViewer
- by Paul F. X. Müller and Gideon Schechtman PDF
- Proc. Amer. Math. Soc. 125 (1997), 2363-2371 Request permission
Abstract:
We introduce a non-standard but, to our opinion natural, order on the initial segments of the Haar system and investigate the isomorphic classification of the linear span, in $L_{p}$, of block bases, with respect to this order.References
- D. L. Burkholder, Distribution function inequalities for martingales, Ann. Probability 1 (1973), 19–42. MR 365692, DOI 10.1214/aop/1176997023
- L. E. Dor and T. Starbird, Projections of $L_{p}$ onto subspaces spanned by independent random variables, Compositio Math. 39 (1979), no. 2, 141–175. MR 546965
- Charles L. Fefferman, The uncertainty principle, Bull. Amer. Math. Soc. (N.S.) 9 (1983), no. 2, 129–206. MR 707957, DOI 10.1090/S0273-0979-1983-15154-6
- W. B. Johnson, B. Maurey, G. Schechtman, and L. Tzafriri, Symmetric structures in Banach spaces, Mem. Amer. Math. Soc. 19 (1979), no. 217, v+298. MR 527010, DOI 10.1090/memo/0217
- Paul F. X. Müller, A local version of a result of Gamlen and Gaudet, Israel J. Math. 63 (1988), no. 2, 212–222. MR 968539, DOI 10.1007/BF02765039
- E.M. Semenov, On the equivalence in $L_{p}$ of rearrangements of the Haar system, English translation in Soviet Math. Dokl. 19 (1978), 1292-1294.
Additional Information
- Paul F. X. Müller
- Affiliation: Institut für Mathematik, J. Kepler Universität, 4040 Linz, Austria
- Address at time of publication: Department of Mathematics, Yale University, 10 Hill House Avenue, New Haven, Connecticut 06520
- MR Author ID: 240120
- Email: paul.mueller@jk.uni-linz.ac.at, muller@math.yale.edu
- Gideon Schechtman
- Affiliation: Department of Theoretical Mathematics, The Weizmann Institute of Science, Rehovot 76100, Israel
- MR Author ID: 155695
- Email: mtschech@weizmann.weizmann.ac.il
- Received by editor(s): September 5, 1995
- Received by editor(s) in revised form: February 23, 1996
- Additional Notes: The first author was supported by the Austrian Academy of Sciences (APART Program). The second author was supported in part by BSF. Both authors participated in the Workshop in Linear Analysis and Probability, Texas A&M University.
- Communicated by: Dale Alspach
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 2363-2371
- MSC (1991): Primary 46B07, 60G42
- DOI: https://doi.org/10.1090/S0002-9939-97-03860-4
- MathSciNet review: 1389531