Another Note on the Embedding of the Sobolev Space for the Limiting Exponent

The embedding of the Sobolev spaces $W_p^s(\mathbb{R}^n)$ in a Lizorkin-type space of locally summable functions of zero smoothness is established. This result is extended to the case of the embedding of Sobolev spaces on nonregular domains of $n$-dimensional Euclidean space. The formulation of the theorem depends on the geometric parameters of the domain of the functions.