On the Interplay of Regularity and Decay in Case of Radial Functions II. Homogeneous Spaces

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• 作者：Winfried Sickel (1) winfried.sickel@uni-jena.de
  Leszek Skrzypczak (2) lskrzyp@amu.edu.pl
• 关键词：Radial functions – ; Homogeneous Besov and Triebel ; Lizorkin spaces – ; Compact embeddings
• 刊名：Journal of Fourier Analysis and Applications
• 出版年：2012
• 出版时间：June 2012
• 年：2012
• 卷：18
• 期：3
• 页码：548-582
• 全文大小：668.7 KB
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• 作者单位：1. Mathematisches Institut, Friedrich-Schiller-Universit盲t Jena, Ernst-Abbe-Platz 2, 07743 Jena, Germany2. Faculty of Mathematics and Computer Science, Adam Mickiewicz University Pozna艅, Ul. Umultowska 87, 61-614 Pozna艅, Poland
• 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 deal with decay and boundedness properties of elements of radial subspaces of homogeneous Besov and Triebel-Lizorkin spaces. For the region of parameters which are of interest for us these homogeneous spaces are larger than the inhomogeneous counterparts. By switching from the inhomogeneous spaces to the homogeneous classes the properties of the radial elements change. Our investigations are based on the atomic decompositions for radial subspaces in the sense of Epperson and Frazier (J. Fourier Anal Appl. 1:311–353, 1995). Finally, we apply these results for deriving some assertions on compact embeddings on unbounded domains.