Spaces of generalized smoothness in the critical case: Optimal embeddings, continuity envelopes and approximation numbers

作者：Moura Susana D; Neves Julio S^*; Schneider Cornelia

来源：Journal of Approximation Theory, 2014, 187: 82-117.

DOI：10.1016/j.jat.2014.07.010

• Function spaces of generalized smoothness
• Optimal embeddings
• Continuity envelopes
• Approximation numbers

We study necessary and sufficient conditions for embeddings of Besov spaces of generalized smoothness B-p,q(sigma,N) (R-n) into generalized Holder spaces Lambda(mu(center dot))(infinity,r) (R-n) when (s) under bar (N tau(-1)) %26gt; 0 and tau(-1) is an element of l(q%26apos;), where tau = sigma N-n/p. A borderline situation, corresponding to the limiting situation in the classical case, is included and give new results. In particular, we characterize optimal embeddings for B-spaces. %26lt;br%26gt;As immediate applications of our results we obtain continuity envelopes and give upper and lower estimates for approximation numbers for the related embeddings. %26lt;br%26gt;We also consider the analogous results for the Triebel-Lizorkin spaces of generalized smoothness F-p,q(sigma,N) (R-n).

• 出版日期2014-11