Limiting embeddings in smoothness Money spaces, continuity envelopes and applications

作者：Yuan, Wen; Haroske, Dorothee D.; Moura, Susana D.; Skrzypczak, Leszek; Yang, Dachun^*

来源：Journal of Approximation Theory, 2015, 192: 306-335.

DOI：10.1016/j.jat.2014.12.006

• Besov-type space
• Limiting embedding
• Morrey space
• Approximation number
• Continuity envelope
• Hardy inequality
• Franke-Jawerth embedding
• Wavelet characterization

In this paper, the authors prove some Franke-Jawerth embedding for the Besov-type spaces B-p,q(s,tau)(R-n) and the Triebel-Lizorkin-type spaces F-p,q(s,tau) (R-n). By using some limiting embedding properties of these spaces and the Besov-Morrey spaces N-u,p,q(s)(R-n), the continuity envelopes in B-p,q(s,tau)(R-n), F-p,q(s,tau)(R-n) and N-u,p,q(s)(R-n) are also worked out. As applications, the authors present some Hardy type inequalities in the scales of B-p,q(s,tau)(R-n), F-p,q(s,tau)(R-n) and N-u,p,q(s)(R-n), and also give the estimates for approximation numbers of the embeddings from B-p,q(s,tau)(Omega), F-p,q(s,tau)(Omega) and N-u,p,q(s)(Omega) into C(Omega), where Omega denotes the unit ball in R-n.

• 出版日期2015-4
• 单位北京师范大学