Acta mathematica scientia,Series B ›› 2013, Vol. 33 ›› Issue (2): 430-442.doi: 10.1016/S0252-9602(13)60010-7

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MULTIPLIER OPERATORS AND EXTREMAL FUNCTIONS RELATED TO THE DUAL DUNKL-SONINE OPERATOR

Fethi SOLTANI   

  1. Higher College of Technology and Informatics, Street of the Employers 45, Charguia 2 - 2035 Tunis, Tunisia
  • Received:2010-07-20 Revised:2012-02-03 Online:2013-03-20 Published:2013-03-20
  • Supported by:

    The author is partially supported by DGRST project 04/UR/15-02 and CMCU program 10G 1503.

Abstract:

We study the dual Dunkl-Sonine operator tSk,? on Rd, and give expression of tSk,?, using Dunkl multiplier operators on Rd. Next, we study the extremal functions f *λλ > 0 related to the Dunkl multiplier operators, and more precisely show that {f * λ}λ>0 converges uniformly to tSk,?(f) as λ →0+. Certain examples based on Dunkl-heat and Dunkl-Poisson kernels are provided to illustrate the results.

Key words: Dunkl transform, dual Dunkl-Sonine operator, multiplier operators, extremal function

CLC Number: 

  • 42B10
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