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Real interpolation of vector-valued spaces in non-diagonal case

Authors: Irina Asekritova and Natan Krugljak
Journal: Proc. Amer. Math. Soc. 133 (2005), 1665-1675
MSC (2000): Primary 46B70; Secondary 46E30
Published electronically: December 20, 2004
MathSciNet review: 2120255
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Abstract: It is shown that the formula

\begin{displaymath}(l_{p_{0}}^{s_{0}}(A_{0}),...,l_{p_{n}}^{s_{n}}(A_{n})) _{\vec{\theta },q} =l_{q}^{s}((A_{0},...,A_{n})_{\vec{\theta},q}), \end{displaymath}

where $\vec{\theta}=(\theta _{0},...,\theta _{n})$ and $s=\theta _{0}s_{0}+...+\theta _{n}s_{n}$ is correct under the restrictions $ A_{n-1}=A_{n}$ and $s_{n-1}\neq s_{n}.$ It is also true if we suppose that

\begin{displaymath}A_{n}=(A_{0},A_{1},...,A_{n-1})_{\vec{\lambda},p},s_{n}\neq \lambda _{0}s_{0}+\lambda _{1}s_{1}+...+\lambda _{n-1}s_{n-1}, \end{displaymath}

and the spaces $A_{0},A_{1},...,A_{n-1}$ are functional Banach or quasi-Banach lattices on the same measure space $(\Omega ,\mu ).$

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

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Additional Information

Irina Asekritova
Affiliation: School of Mathematics and Systems Engineering, Vaxjo University, SE 351 93, Vaxjo, Sweden

Natan Krugljak
Affiliation: Department of Mathematics, LuleåUniversity of Technology, SE 972 33, Luleå, Sweden

Keywords: Real interpolation, vector-valued spaces
Received by editor(s): September 16, 2003
Published electronically: December 20, 2004
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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