Embeddings of Besov–Morrey spaces on bounded domains

Volume 218 / 2013

Dorothee D. Haroske, Leszek Skrzypczak Studia Mathematica 218 (2013), 119-144 MSC: Primary 46E35. DOI: 10.4064/sm218-2-2


We study embeddings of spaces of Besov–Morrey type, $\mathop {\rm id}\nolimits _\varOmega : {{\cal N}^{s_1}_{p_1,u_1,q_1}}(\varOmega ) \hookrightarrow {{\cal N}^{s_2}_{p_2,u_2,q_2}}(\varOmega )$, where $\varOmega \subset {\mathbb R}^{d}$ is a bounded domain, and obtain necessary and sufficient conditions for the continuity and compactness of $\mathop {\rm id}\nolimits _\varOmega $. This continues our earlier studies relating to the case of ${\mathbb R}^{d}$. Moreover, we also characterise embeddings into the scale of $L_p$ spaces or into the space of bounded continuous functions.


  • Dorothee D. HaroskeMathematical Institute
    Friedrich-Schiller-University Jena
    D-07737 Jena, Germany
  • Leszek SkrzypczakFaculty of Mathematics & Computer Science
    Adam Mickiewicz University
    Umultowska 87
    61-614 Poznań, Poland

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