Embeddings and the growth envelope of Besov spaces involving only slowly varying smoothness

0363305 - MÚ 2012 RIV US eng J - Journal Article
Caetano, A.M. - Gogatishvili, Amiran - Opic, B.
Embeddings and the growth envelope of Besov spaces involving only slowly varying smoothness.
Journal of Approximation Theory. Roč. 163, č. 10 (2011), s. 1373-1399. ISSN 0021-9045. E-ISSN 1096-0430
R&D Projects: GA ČR GA201/05/2033; GA ČR GA201/08/0383
Institutional research plan: CEZ:AV0Z10190503
Keywords : Besov spaces with generalized smoothness * classical Lorentz spaces * Lorentz-Karamata spaces * sharp embeddings * growth envelopes
Subject RIV: BA - General Mathematics
Impact factor: 0.681, year: 2011
http://www.sciencedirect.com/science/article/pii/S002190451100061X

We characterize local embeddings of Besov spaces B^{0,b}_{p,r} involving only a slowly varying smoothness b into classical Lorentz spaces. These results are applied to establish sharp local embeddings of the Besov spaces in question into Lorentz–Karamata spaces. As a consequence of these results, we are able to determine growth envelopes of spaces B^{0,b}_{p,r} and to show that we cannot describe all local embeddings of Besov spaces B^{0,b}_{p,r} into Lorentz–Karamata spaces in terms of growth envelopes.
Permanent Link: http://hdl.handle.net/11104/0199284