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On $ (L\sp{po}(A\sb{o}),\,\ L\sp{p\sb{1}}(A\sb{1}))\sb{\theta },\,\sb{q}$


Author: Michael Cwikel
Journal: Proc. Amer. Math. Soc. 44 (1974), 286-292
MSC: Primary 46E30
DOI: https://doi.org/10.1090/S0002-9939-1974-0358326-0
MathSciNet review: 0358326
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Abstract: The Lions-Peetre formula for $ {({L^{{p_0}}}({A_0}),{L^{{p_1}}}({A_1}))_{\theta ,q}}$ valid for $ q = p(\theta )$, where $ 1/p(\theta ) = (1 - \theta )/{p_0} + \theta /{p_1}$, is shown to have no reasonable generalization for any $ q \ne p(\theta )$.


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

  • [1] P. L. Butzer and H. Berens, Semi-groups of operators and approximation, Die Grundlehren der math. Wissenschaften, Band 145, Springer-Verlag, New York, 1967. MR 37 #5588. MR 0230022 (37:5588)
  • [2] R. A. Hunt, On $ L(p,q)$ spaces, Enseignement Math. (2) 12 (1966), 249-276. MR 36 #6921. MR 0223874 (36:6921)
  • [3] J. L. Lions and J. Peetre, Sur une classe d'espaces d'interpolation, Inst. Hautes Etudes Sci. Publ. Math. No. 19 (1964), 5-68. MR 29 #2627. MR 0165343 (29:2627)
  • [4] Y. Sagher, Interpolation of $ r$-Banach spaces, Studia Math. 41 (1972), 45-70. MR 0306895 (46:6016)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0358326-0
Keywords: Interpolation spaces, vector-valued $ {L^p}$ space, $ L(p,q)$ space
Article copyright: © Copyright 1974 American Mathematical Society

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