Generalized Hausdorff Operators on K̇α,qβ,pℝ and HK̇α,qβ,p,Nℝ in the Dunkl Settings

Abstract

In the present paper, we obtain some new results, and we generalize some known results for the Hausdorff operators. We have studied the generalized Hausdorff operators Hα,φ on the Dunkl-type homogeneous weighted Herz spaces K̇α,qβ,pℝ and Dunkl Herz-type Hardy spaces HK̇α,qβ,p,Nℝ. We have determined simple sufficient conditions for these operators to be bounded on these spaces. As applications, we provide necessary and sufficient conditions for generalized Cesàro operator to be bounded on K̇α,qβ,pℝ and Hardy inequality for K̇α,qβ,pℝ.