An elementary proof of the Brezis and Mironescu theorem on the composition operator in fractional Sobolev spaces

On the Bourgain, Brezis, and Mironescu T

On the Bourgain, Brezis, and Mironescu Theorem Concerning Limiting Embeddings of Fractional Sobolev Spaces

✍ V. Maz'ya; T. Shaposhnikova 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 112 KB

The article is concerned with the Bourgain, Brezis and Mironescu theorem on the asymptotic behaviour of the norm of the Sobolev-type embedding operator: W s;p ! L pn=ðnÀspÞ as s " 1 and s " n=p: Their result is extended to all values of s 2 ð0; 1Þ and is supplied with an elementary proof. The relati