Multiplier operators and extremal functions related to the dual dunkl-sonine operator

We study the dual Dunkl-Sonine operator tSk,ℓ on ℝd, and give expression of tSk,ℓ, 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,ℓ(f) as λ → 0+. Certain examples based on Dunkl-heat and Dunkl-Poisson kernels are provided to illustrate the results.