Refined Sobolev Inequalities in Lorentz Spaces

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• 作者：1. Centre de Mathématiques ; Faculté de Sciences et Technologie ; Université Paris XII ; Val de Marne ; 61 ; avenue du Général de Gaulle ; 94 010 Creteil Cedex ; France2. UMR 7598 ; Laboratoire Jacques-Louis Lions ; UPMC Univ Paris 06 ; 75005 Paris ; France3. UMR 7598 ; Laboratoire Jacques-Louis Lions ; CNRS ; 75005 Paris ; France
• 关键词：Refined Sobolev inequalities – Refined Hardy inequalities – Lorentz spaces – Besov spaces
• 刊名：Journal of Fourier Analysis and Applications
• 出版年：2011
• 出版时间：August 2011
• 年：2011
• 卷：17
• 期：4
• 页码：662-673
• 全文大小：361.8 KB
• 参考文献：1. Bahouri, H., Chemin, J.-Y., Gallagher, I.: Refined Hardy inequalities. Ann. Sc. Norm. Super. Pisa, Cl. Sci. 5, 375–391 (2006)
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• 作者单位：http://www.springerlink.com/content/7768812546784835/
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Fourier Analysis
  Abstract Harmonic Analysis
  Approximations and Expansions
  Partial Differential Equations
  Applications of Mathematics
  Signal,Image and Speech Processing
  
• 出版者：Birkh盲user Boston
• ISSN：1531-5851

文摘

We establish refined Sobolev inequalities between the Lorentz spaces and homogeneous Besov spaces. The sharpness of these inequalities is illustrated on several examples, in particular based on non-uniformly oscillating functions known as chirps. These results are also used to derive refined Hardy inequalities.