JournalsrmiVol. 22, No. 1pp. 305–322

Compact embeddings of Brézis-Wainger type

  • Fernando Cobos

    Universidad Complutense de Madrid, Spain
  • Thomas Kühn

    Universität Leipzig, Germany
  • Tomas Schonbek

    Florida Atlantic University, Boca Raton, USA
Compact embeddings of Brézis-Wainger type cover
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Abstract

Let Ω\Omega be a bounded domain in Rn\mathbb R^n and denote by idΩid_\Omega the restriction operator from the Besov space Bpq1+n/p(Rn)B_{pq}^{1+n/p}(\mathbb R^n) into the generalized Lipschitz space Lip(1,α)(Ω)Lip^{(1,-\alpha)}(\Omega). We study the sequence of entropy numbers of this operator and prove that, up to logarithmic factors, it behaves asymptotically like ek(idΩ)k1/pe_k(id_\Omega) \sim k^{-1/p} if α>max(1+2/p1/q,1/p)\alpha > \max (1+2/p-1/q,1/p). Our estimates improve previous results by Edmunds and Haroske.

Cite this article

Fernando Cobos, Thomas Kühn, Tomas Schonbek, Compact embeddings of Brézis-Wainger type. Rev. Mat. Iberoam. 22 (2006), no. 1, pp. 305–322

DOI 10.4171/RMI/457