Generalized Hausdorff Operators on K̇α, qβ, pℝ and HK̇α, qβ, p, Nℝ in the Dunkl Settings. (29th August 2021)

• Record Type: Journal Article
• Authors: Saadi, Faouaz; Tyr, Othman; Daher, Radouan
• Other Names: Boulaaras Salah Mahmoud Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2021(2021)
• Publication Date: 2021-08-29
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2021/6547407
• Languages: English
• ISSNs: 2314-8896

Abstract

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 H α, φ on the Dunkl-type homogeneous weighted Herz spaces K ̇ α, q β, p ℝ and Dunkl Herz-type Hardy spaces H K ̇ α, q β, p, N ℝ . 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 K ̇ α, q β, p ℝ and Hardy inequality for K ̇ α, q β, p ℝ .