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Some Banach space embeddings of classical function spaces

  • N.L. Carothers (a1) and S.J. Dilworth (a2)
Abstract

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.

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References
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[1]Bergh, J. and Löfstrom, J., Interpolation spaces (Springer-Verlag, New York, 1976).
[2]Carothers, N.L. and Dilworth, S.J., ‘Inequalities for sums of independent random variables’, Proc. Amer. Math. Soc. 104 (1988), 221226.
[3]Carothers, N.L. and Dilworth, S.J., ‘Subspaces of Lp, q’, Proc. Amer. Math. Soc. 104 (1988), 537545.
[4]Dilworth, S.J., ‘A scale of linear spaces related to the Lp scale’, Illinois J. Math, (to appear).
[5]Guerre, S. and Levy, M., ‘Espaces lp dans les sous-espaces de L1‘, Trans. Amer. Math. Soc. 279 (1983), 611616.
[6]Johnson, W.B., Maurey, B., Schechtman, G. and Tzafriri, L., ‘Symmetric structures in Banach spaces’, Mem. Amer. Math. Soc. 217 (1979).
[7]Johnson, W.B. and Schechtman, G., ‘Sums of independent random variables in rearrangement invariant function spaces’, Ann. Probab. 17 (1989), 789808.
[8]Lindenstrauss, J. and Tzafriri, L., Classical Banach spaces II. Function Spaces (Springer-Verlag, New York, 1979).
[9]Rosenthal, H.P., ‘On the subspaces of Lp (p > 2) spanned by sequences of independent random variables’, Israel J. Math. 8 (1970), 273303.
[10]Schütt, C., ‘Lorentz spaces that are isomorphic to subspaces of L1’, Trans. Amer. Math. Soc. 314 (1989), 583595.
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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