Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-22T21:19:10.390Z Has data issue: false hasContentIssue false
  • English
  • Français

Some Banach space embeddings of classical function spaces

Published online by Cambridge University Press:  17 April 2009

N.L. Carothers  and
S.J. Dilworth
N.L. Carothers
Affiliation:
Department of Mathematics and Statistics, Bowling Green State University, Bowling Green OH 43403-0221, United States of America
S.J. Dilworth
Affiliation:
Department of Mathematics, University of South Carolina, Columbia SC 29208, United States of America
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Banach space embeddings of the Orlicz space Lp + Lq and the Lorentz space Lp, q into the Lebesgue-Bochner space Lr(ls) are demonstrated for appropriate ranges of the parameters.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 43 , Issue 1 , February 1991 , pp. 73 - 77
Copyright
Copyright © Australian Mathematical Society 1991

References

[1]Bergh, J. and Löfstrom, J., Interpolation spaces (Springer-Verlag, New York, 1976).CrossRefGoogle Scholar
[2]Carothers, N.L. and Dilworth, S.J., ‘Inequalities for sums of independent random variables’, Proc. Amer. Math. Soc. 104 (1988), 221–226.CrossRefGoogle Scholar
[3]Carothers, N.L. and Dilworth, S.J., ‘Subspaces of Lp, q’, Proc. Amer. Math. Soc. 104 (1988), 537–545.Google Scholar
[4]Dilworth, S.J., ‘A scale of linear spaces related to the Lp scale’, Illinois J. Math, (to appear).Google Scholar
[5]Guerre, S. and Levy, M., ‘Espaces lp dans les sous-espaces de L1‘, Trans. Amer. Math. Soc. 279 (1983), 611–616.Google Scholar
[6]Johnson, W.B., Maurey, B., Schechtman, G. and Tzafriri, L., ‘Symmetric structures in Banach spaces’, Mem. Amer. Math. Soc. 217 (1979).Google Scholar
[7]Johnson, W.B. and Schechtman, G., ‘Sums of independent random variables in rearrangement invariant function spaces’, Ann. Probab. 17 (1989), 789–808.Google Scholar
[8]Lindenstrauss, J. and Tzafriri, L., Classical Banach spaces II. Function Spaces (Springer-Verlag, New York, 1979).CrossRefGoogle Scholar
[9]Rosenthal, H.P., ‘On the subspaces of Lp (p > 2) spanned by sequences of independent random variables’, Israel J. Math. 8 (1970), 273–303.CrossRefGoogle Scholar
[10]Schütt, C., ‘Lorentz spaces that are isomorphic to subspaces of L1’, Trans. Amer. Math. Soc. 314 (1989), 583–595.CrossRefGoogle Scholar