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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
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}_{...{\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)$.

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

  • 1. I. Asekritova and N. Krugljak, Real interpolation of vector-valued spaces in non-diagonal case, Proc. Amer. Math. Soc. 133 (2005), 1665-1675. MR 2120255 (2005k:46047)
  • 2. I. Asekritova, N. Krugljak, L. Maligranda, L. Nikolova, and L.-E. Persson, Lions-Peetre reiteration formulas for triples and their applications, Studia Math. 145 (2001), 219-254. MR 1829209 (2002e:46089)
  • 3. J. Bergh and J. Löfström, Interpolation spaces. An introduction, Grundlehren Math. Wiss., vol. 223, Springer-Verlag, Berlin-New York, 1976. MR 0482275 (58:2349)
  • 4. R. DeVore and V. Popov, Interpolation of approximation spaces, Constructive Theory of Functions (Varna, 1987), Bulgar. Acad. Sci., Sofia, 1988, pp. 110-119. MR 994826 (90e:46076)
  • 5. J. E. Gilbert, Interpolation between weighted $ L^p$-spaces, Ark. Mat. 10 (1972), 235-249. MR 0324393 (48:2745)
  • 6. G. Sparr, Interpolation of several Banach spaces, Ann. Mat. Pura Appl. (4) 99 (1974), 247-316. MR 0372641 (51:8848)

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Additional Information

I. Asekritova
Affiliation: School of Mathematics and System Engineering, Växjö University, Sweden

N. Kruglyak
Affiliation: Department of Mathematics, Lulea University of Technology, Sweden

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

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