Another note on the embedding of the Sobolev space for the limiting exponent

Abstract

The embedding of the Sobolev spaces W_p^s (ℝⁿ) 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.