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

摘要

We study the dual Dunkl-Sonine operator tSk, on Rd , and give expression of tSk,e1 , using Dunkl multiplier operators on R d . Next, we study the extremal functions fμλ , λ> 0 related to the Dunkl multiplier operators, and more precisely show that {fμλ}λ>0 converges uniformly to tSk,e(f) as λ→ 0 + . Certain examples based on Dunkl-heat and Dunkl-Poisson kernels are provided to illustrate the results.