On $(L^{po}(A_{o}), \ L^{p_{1}}(A_{1}))_{\theta }, _{q}$
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- by Michael Cwikel
- Proc. Amer. Math. Soc. 44 (1974), 286-292
- DOI: https://doi.org/10.1090/S0002-9939-1974-0358326-0
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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
- Paul L. Butzer and Hubert Berens, Semi-groups of operators and approximation, Die Grundlehren der mathematischen Wissenschaften, Band 145, Springer-Verlag New York, Inc., New York, 1967. MR 0230022, DOI 10.1007/978-3-642-46066-1
- Richard A. Hunt, On $L(p,\,q)$ spaces, Enseign. Math. (2) 12 (1966), 249–276. MR 223874
- J.-L. Lions and J. Peetre, Sur une classe d’espaces d’interpolation, Inst. Hautes Études Sci. Publ. Math. 19 (1964), 5–68 (French). MR 165343, DOI 10.1007/BF02684796
- Yoram Sagher, Interpolation of $r$-Banach spaces, Studia Math. 41 (1972), 45–70. MR 306895, DOI 10.4064/sm-41-1-45-70
Bibliographic Information
- © Copyright 1974 American Mathematical Society
- 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