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

作者：Caetano Antonio M^*; Gogatishvili Amiran; Opic Bohumir

来源：Journal of Approximation Theory, 2011, 163(10): 1373-1399.

DOI：10.1016/j.jat.2011.03.005

• Besov spaces with generalized smoothness
• Classical Lorentz spaces
• Lorentz-Karamata spaces
• Sharp embeddings
• Growth envelopes

We characterize local embeddings of Besov spaces B(p,r)(0,b) 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(p,r)(0,b) and to show that we cannot describe all local embeddings of Besov spaces B(p,r)(0,b) into Lorentz-Karamata spaces in terms of growth envelopes.

• 出版日期2011-10