Abstract
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 \({{\mathbf W}^m_p ({\mathbb R}^n)}\).
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Triebel, H. Limits of Besov norms. Arch. Math. 96, 169–175 (2011). https://doi.org/10.1007/s00013-010-0214-1
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DOI: https://doi.org/10.1007/s00013-010-0214-1