Espace de Dixmier des opérateurs de Hankel sur les espaces de Bergman à poids

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• 作者：Romaric Tytgat
• 关键词：Hankel operator ; Dixmier trace ; Bergman space ; 47B35 ; 32A36 ; 32A37 ; 47B10
• 刊名：Czechoslovak Mathematical Journal
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：65
• 期：2
• 页码：399-426
• 全文大小：235 KB
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• 作者单位：Romaric Tytgat (1)
  
  1. Centre de Mathématiques et Informatique (CMI), Aix-Marseille Université, Technop?le Chateau-Gombert, 39 Rue F. Joliot Curie, 134 53, Marseille Cedex 13, France
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Analysis
  Convex and Discrete Geometry
  Ordinary Differential Equations
  Mathematical Modeling and IndustrialMathematics
  
• 出版者：Springer Netherlands
• ISSN：1572-9141

文摘

In this paper, we give theoretical results on Macaev ideal and Dixmier trace. Then we give a characterization of antiholomorphic symbols \(\overline f \) such that the Hankel operator \({H_{\overline f }}\) on a Bergman weighted space is in an ideal of Macaev and we give the Dixmier trace. For this, we look at the behavior of Schatten’s norms \(\mathcal{S}^p\) when p tends to 1, using results of Engli? and Rochberg on Bergman space. We also give results on powers of such operators.