Embedding of Sobolev Space in the Case of the Limit Exponent

O. V. Besov

Matematičeskie zametki, Tome 98 (2015) no. 4, pp. 498-510

Résumé

We establish the embeddings of the Sobolev space $W_p^s$ and the space $B_{pq}^s$ (in the case of the limit exponent) in the spaces of locally summable functions of zero smoothness. This refines the embeddings of the Sobolev space in the Lorentz space and in the Lorentz–Zygmund space. The relationship between the Lorentz spaces and the corresponding spaces of functions of zero smoothness is established. Similar embeddings of the spaces of potentials are determined.

Détail

Keywords: Sobolev space $W_p^s$, the space $B_{pq}^s$, locally summable function of zero smoothness, Lorentz space, Lorentz–Zygmund space, space of potentials.