Real interpolation of vector-valued spaces in non-diagonal case
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- by Irina Asekritova and Natan Krugljak
- Proc. Amer. Math. Soc. 133 (2005), 1665-1675
- DOI: https://doi.org/10.1090/S0002-9939-04-07714-7
- Published electronically: December 20, 2004
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Abstract:
It is shown that the formula \begin{equation*} (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{equation*} 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{equation*} 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{equation*} 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
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Bibliographic Information
- Irina Asekritova
- Affiliation: School of Mathematics and Systems Engineering, Vaxjo University, SE 351 93, Vaxjo, Sweden
- Email: irina.asekritova@msi.vxu.se
- Natan Krugljak
- Affiliation: Department of Mathematics, LuleåUniversity of Technology, SE 972 33, Luleå, Sweden
- Email: natan@sm.luth.se
- Received by editor(s): September 16, 2003
- Published electronically: December 20, 2004
- Communicated by: N. Tomczak-Jaegermann
- © Copyright 2004
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 133 (2005), 1665-1675
- MSC (2000): Primary 46B70; Secondary 46E30
- DOI: https://doi.org/10.1090/S0002-9939-04-07714-7
- MathSciNet review: 2120255