Archiv der Mathematik

, Volume 96, Issue 2, pp 169–175 | Cite as

Limits of Besov norms

  • Hans Triebel


Besov spaces \({{\mathbf B}^s_{p,q} ({\mathbb R}^n)}\) with s > 0 can be normed in terms of the differences \({\Delta^m_h f}\) and related moduli of smoothness ω m (f, t) p , where \({0 < s < m \in {\mathbb N}}\). The paper deals with the question what happens if \({s {\uparrow} m}\) and how the outcome is related to the Sobolev spaces \({{\mathbf W}^m_p ({\mathbb R}^n)}\).

Mathematics Subject Classification (2000)



Besov spaces Sobolev spaces Limiting embeddings 


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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Mathematisches Institut, Fakultät für Mathematik und InformatikFriedrich-Schiller-Universität JenaJenaGermany

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