Acta mathematica scientia, Series B >
MULTIPLIER OPERATORS AND EXTREMAL FUNCTIONS RELATED TO THE DUAL DUNKL-SONINE OPERATOR
Received date: 2010-07-20
Revised date: 2012-02-03
Online published: 2013-03-20
Supported by
The author is partially supported by DGRST project 04/UR/15-02 and CMCU program 10G 1503.
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 *λ, λ > 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.
Fethi SOLTANI . MULTIPLIER OPERATORS AND EXTREMAL FUNCTIONS RELATED TO THE DUAL DUNKL-SONINE OPERATOR[J]. Acta mathematica scientia, Series B, 2013 , 33(2) : 430 -442 . DOI: 10.1016/S0252-9602(13)60010-7
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