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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

 

 

Interpolation of Besov spaces in the nondiagonal case


Authors: I. Asekritova and N. Kruglyak
Translated by: S. V. Kislyakov
Original publication: Algebra i Analiz, tom 18 (2006), nomer 4.
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
Published electronically: May 25, 2007
MathSciNet review: 2262581
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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

$\displaystyle (l^{\bar s_0}_{q_0}((X_0,X_1)_{\eta_0,p_0}),\dots, l^{\bar s_n}_{... ...ar{\theta},q}= l^{\bar s_{\bar{\theta}}}_q((X_0,X_1)_{\eta_{\bar{\theta}},q}), $

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)$.


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Additional 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

DOI: https://doi.org/10.1090/S1061-0022-07-00958-2
Keywords: Real interpolation, vector-valued spaces, Besov spaces
Received by editor(s): January 21, 2006
Published electronically: May 25, 2007
Article copyright: © Copyright 2007 American Mathematical Society