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Embeddings of Sobolev-type spaces into generalized H?lder spaces involving \(k\)
- 作者：Amiran Gogatishvili ; Susana D. Moura…
- 关键词：Rearrangement ; invariant Banach function space ; Modulus of smoothness ; Distributional gradient ; Lorentz space ; Sobolev ; type space ; Banach lattice ; H?lder ; type space ; Embeddings ; 26D15 ; 26B35 ; 26A15 ; 26A16 ; 46E30 ; 46E35 ; 46B42
- 刊名：Annali di Matematica Pura ed Applicata
- 出版年：2015
- 出版时间：April 2015
- 年：2015
- 卷：194
- 期：2
- 页码：425-450
- 全文大小：352 KB
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18. Gogatishvili, A, Neves, JS, Opic, B (2010) Optimal embeddings of Bessel-potential-type spaces into generalized H?lder spaces involving $$k$$ k -modulus of smoothness. Potential Anal. 32: pp. 201-228 CrossRef
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20. Gogatishvili, A, Neves, JS, Opic, B (2011) Compact embeddings of Bessel-potential-type spaces into generalized H?lder spaces involving $$k$$ k -modulus of smoothness. Z. Anal. Anwendungen 30: pp. 1-27 CrossRef
21. Gogatishvili, A., Opic, B., Trebels, W.: Limiting reiteration for real interpolation with slowly varying functions. Math. Nachr. - 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Mathematics
- 出版者：Springer Berlin / Heidelberg
- ISSN：1618-1891
文摘
We use an estimate of the \(k\) -modulus of smoothness of a function \(f\) such that the norm of its distributional gradient \(|\nabla ^kf|\) belongs locally to the Lorentz space \(L^{n/k, 1}({\mathbb {R}}^n),\,k \in {\mathbb {N}},\,k\le n\) , and we prove its reverse form to establish necessary and sufficient conditions for continuous embeddings of Sobolev-type spaces. These spaces are modelled upon rearrangement-invariant Banach function spaces \(X({\mathbb {R}}^n)\) . Target spaces of our embeddings are generalized H?lder spaces defined by means of the \(k\) -modulus of smoothness \((k\in {\mathbb {N}})\) . General results are illustrated with examples.
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