Spaces of generalized smoothness in the critical case: Optimal embeddings, continuity envelopes and approximation numbers
| Autor: | Júlio S. Neves, Susana D. Moura, Cornelia Schneider |
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| Rok vydání: | 2014 |
| Předmět: |
Approximation numbers
Numerical Analysis Smoothness (probability theory) Optimal embeddings Applied Mathematics General Mathematics 010102 general mathematics Continuity envelopes 010103 numerical & computational mathematics Limiting 01 natural sciences Combinatorics Function spaces of generalized smoothness 0101 mathematics Analysis Mathematics |
| Zdroj: | Repositório Científico de Acesso Aberto de Portugal Repositório Científico de Acesso Aberto de Portugal (RCAAP) instacron:RCAAP |
| ISSN: | 0021-9045 |
| DOI: | 10.1016/j.jat.2014.07.010 |
| Popis: | We study necessary and sufficient conditions for embeddings of Besov spaces of generalized smoothness B p , q ? , N ( R n ) into generalized Holder spaces ? ∞ , r µ ( ? ) ( R n ) when s ? ( N ? - 1 ) 0 and ? - 1 ? ? q ' , where ? = ? 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.As immediate applications of our results we obtain continuity envelopes and give upper and lower estimates for approximation numbers for the related embeddings.We also consider the analogous results for the Triebel-Lizorkin spaces of generalized smoothness F p , q ? , N ( R n ) . |
| Databáze: | OpenAIRE |
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