Riesz Transforms Characterizations of Hardy Spaces \(H^1\) for the Rational Dunkl Setting and Multidimensional Bessel Operators

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• 作者：Jacek Dziubański
• 关键词：Dunkl theory ; Riesz transform ; Hardy space ; Maximal operator ; Atomic decomposition
• 刊名：Journal of Geometric Analysis
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：26
• 期：4
• 页码：2639-2663
• 全文大小：574 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Differential Geometry
  Convex and Discrete Geometry
  Fourier Analysis
  Abstract Harmonic Analysis
  Dynamical Systems and Ergodic Theory
  Global Analysis and Analysis on Manifolds
  
• 出版者：Springer New York
• ISSN：1559-002X
• 卷排序：26

文摘

We characterize the Hardy space \(H^1\) in the rational Dunkl setting associated with the reflection group \(\mathbb {Z}_2^n\) by means of special Riesz transforms. As a corollary we obtain Riesz transforms characterization of \(H^1\) for product of Bessel operators in \((0,\infty )^n\).