Interpolation of Besov spaces in the nondiagonal case
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I. Asekritova and N. Kruglyak
Translated by: S. V. Kislyakov - St. Petersburg Math. J. 18 (2007), 511-516
- DOI: https://doi.org/10.1090/S1061-0022-07-00958-2
- Published electronically: May 25, 2007
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Abstract:
In the nondiagonal case, interpolation spaces for a collection of Besov spaces are described. The results are consequences of the fact that, whenever the convex hull of points $(\bar s_0,\eta _0),\dots ,(\bar s_n,\eta _n)\in \mathbb R^{m+1}$ includes a ball of $\mathbb R^{m+1}$, we have \begin{equation*} (l^{\bar s_0}_{q_0}((X_0,X_1)_{\eta _0,p_0}),\dots , l^{\bar s_n}_{q_n}((X_0,X_1)_{\eta _n,p_n}))_{\bar {\theta },q}= l^{\bar s_{\bar {\theta }}}_q((X_0,X_1)_{\eta _{\bar {\theta }},q}), \end{equation*} where $\bar \theta =(\theta _0,\dots ,\theta _n)$ and $(s_{\bar {\theta }},\eta _{\bar {\theta }})=\theta _0(\bar s_0, \eta _0)+\dots +\theta _n(\bar s_n,\eta _n)$.References
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Bibliographic Information
- I. Asekritova
- Affiliation: School of Mathematics and System Engineering, Växjö University, Sweden
- Email: irina.asekritova@vxu.se
- N. Kruglyak
- Affiliation: Department of Mathematics, Lulea University of Technology, Sweden
- Email: natan@ltu.se
- Received by editor(s): January 21, 2006
- Published electronically: May 25, 2007
- © Copyright 2007 American Mathematical Society
- Journal: St. Petersburg Math. J. 18 (2007), 511-516
- MSC (2000): Primary 46B70; Secondary 46E30
- DOI: https://doi.org/10.1090/S1061-0022-07-00958-2
- MathSciNet review: 2262581