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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

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
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 )$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1974-0358326-0
PII: S 0002-9939(1974)0358326-0
Keywords: Interpolation spaces, vector-valued $ {L^p}$ space, $ L(p,q)$ space
Article copyright: © Copyright 1974 American Mathematical Society