Embeddings of Besov–Morrey spaces on bounded domains

Dorothee D. Haroske ¹   ; Leszek Skrzypczak ²

¹ Mathematical Institute Friedrich-Schiller-University Jena D-07737 Jena, Germany
² Faculty of Mathematics & Computer Science Adam Mickiewicz University Umultowska 87 61-614 Poznań, Poland

Studia Mathematica, Tome 218 (2013) no. 2, pp. 119-144

Résumé

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.

Détail

DOI : 10.4064/sm218-2-2

Keywords: study embeddings spaces besov morrey type mathop nolimits varomega cal varomega hookrightarrow cal varomega where varomega subset mathbb bounded domain obtain necessary sufficient conditions continuity compactness mathop nolimits varomega continues earlier studies relating nbsp mathbb moreover characterise embeddings scale spaces space bounded continuous functions