Embedding of Sobolev Space in the Case of the Limit Exponent

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.