1Sudan University of Science and Technology, College of Education, Department of Mathematics, Sudan
2Qassim University, College of Science & Arts, Department of Mathematics, Saudi Arabia
3University of Bakht Er-Ruda, College of Education, Department of Mathematics, Sudan
Online published on 4 January, 2021.
In this paper we give overview results about the Bourgain, Brezis, and Mironescu theorem regarding limiting embeddings of fractional Sobolev spaces. We give this theorem on the asymptotic behaviour of the norm of the Sobolev-type embedding operator: W01−ε,1+ε→Ln(1+ε)(n−(1−ε2) as ε↑0 and 1−ε ↑n(1+ε). We extended results of this theorem for all values of 1−εε 0,1.
Embeddings, Sobolev spaces, Bourgain
