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Journal d’Analyse Mathématique

, Volume 97, Issue 1, pp 25–55 | Cite as

Convolution operator and maximal function for the Dunkl transform

  • Sundaram Thangavelu
  • Yuan Xu
Article

Abstract

For a family of weight functionsh K invariant under a finite reflection group onR d, analysis related to the Dunkl transform is carried out for the weightedL p spaces. Making use of the generalized translation operator and the weighted convolution, we study the summability of the inverse Dunkl transform, including as examples the Poisson integrals and the Bochner-Riesz means. We also define a maximal function and use it to prove the almost everywhere convergence.

Keywords

Explicit Formula Heat Kernel Maximal Function Radial Function Weak Type 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© The Hebrew University Magnes Press 2005

Authors and Affiliations

  • Sundaram Thangavelu
    • 1
  • Yuan Xu
    • 2
  1. 1.Stat-Math DivisionIndian Statistical InstituteBangaloreIndia
  2. 2.Department of MathematicsUniversity of OregonEugeneUSA

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