The Hardy Space \(H^1\) in the Rational Dunkl Setting

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• 作者：Jean-Philippe Anker ; Néjib Ben Salem ; Jacek Dziubański…
• 关键词：Dunkl theory ; Heat kernel ; Hardy space ; Maximal operator ; Atomic decomposition ; Multiplier ; Primary ; 42B30 ; Secondary ; 33C52 ; 33C67 ; 33D67 ; 33D80 ; 35K08 ; 42B25 ; 42C05
• 刊名：Constructive Approximation
• 出版年：2015
• 出版时间：August 2015
• 年：2015
• 卷：42
• 期：1
• 页码：93-128
• 全文大小：638 KB
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• 作者单位：Jean-Philippe Anker (1)
  Néjib Ben Salem (2)
  Jacek Dziubański (3)
  Nabila Hamda (2)
  
  1. Fédération Denis Poisson (FR 2964) & Laboratoire MAPMO (UMR 7349), Université d’Orléans & CNRS, Batiment de mathématiques, B.P. 6759, 45067?, Orléans Cedex 2, France
  2. Faculté des Sciences de Tunis, Université de Tunis El Manar, LR11ES11 Analyse Mathématiques et Applications, 2092, Tunis, Tunisia
  3. Instytut Matematyczny, Uniwersytet Wroc?awski, Pl. Grunwaldzki 2/4, 50-384, Wroc?aw, Poland
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Numerical Analysis
  Analysis
  
• 出版者：Springer New York
• ISSN：1432-0940

文摘

This paper is perhaps the first attempt at a study of the Hardy space \(H^1\) in the rational Dunkl setting. Following Uchiyama’s approach, we characterize \(H^1\) atomically and by means of the heat maximal operator. We also obtain a Fourier multiplier theorem for \(H^1\). These results are proved here in the one-dimensional case and in the product case.