On mappings generating the embeddings of Sobolev spaces
β Scribed by A. D. Ukhlov
- Publisher
- SP MAIK Nauka/Interperiodica
- Year
- 1992
- Tongue
- English
- Weight
- 400 KB
- Volume
- 34
- Category
- Article
- ISSN
- 0037-4466
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract We study the Riesz potentials __I~Ξ±~f__ on the generalized Lebesgue spaces __L__^__p__(Β·)^(β^__d__^), where 0 < __Ξ±__ < __d__ and __I~Ξ±~f__(__x__) β β« |__f__(__y__)| |__x__ β __y__|^__Ξ±__ β __d__^ __dy__. Under the assumptions that __p__ locally satisfies |__p__(__x__) β __p__(__x__)| β€
## Abstract Let Ξ© be an open subset of β^__n__^ and let __p__ β [1, __n__). We prove that the measure of nonβcompactness of the Sobolev embedding __W__^__k,p__^~0~(Ξ©) β __L__^__p__\*^(Ξ©) is equal to its norm. This means that the entropy numbers of this embedding are constant and equal to the norm.
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=Γ°nΓspΓ as s " 1 and s " n=p: Their result is extended to all values of s 2 Γ°0; 1Γ and is supplied with an elementary proof. The relati