Embedding of Sobolev spaces with limit exponent revisited

Abstract

An embedding of the Sobolev spaces W_p^s (ℝⁿ) in Lizorkin-type spaces of locally integrable functions of smoothness zero is obtained; a similar assertion for Riesz and Bessel potentials is presented. The embedding theorem is extended to Sobolev spaces on irregular domains in n-dimensional Euclidean space. The statement of the theorem depends on geometric parameters of the domain of functions.