Generalized Hausdorff Operators on K̇α,qβ,pℝ and HK̇α,qβ,p,Nℝ in the Dunkl Settings
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...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
|
| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2021/6547407 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832556623947628544 |
|---|---|
| author | Faouaz Saadi Othman Tyr Radouan Daher |
| author_facet | Faouaz Saadi Othman Tyr Radouan Daher |
| author_sort | Faouaz Saadi |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-9a1f20668e3245be8d0f203aa5e64558 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-9a1f20668e3245be8d0f203aa5e645582025-02-03T05:44:50ZengWileyJournal of Function Spaces2314-88962314-88882021-01-01202110.1155/2021/65474076547407Generalized Hausdorff Operators on K̇α,qβ,pℝ and HK̇α,qβ,p,Nℝ in the Dunkl SettingsFaouaz Saadi0Othman Tyr1Radouan Daher2Department of Mathematics, Laboratory of Topology, Algebra, Geometry, and Discrete Mathematics, Faculty of Sciences Aïn Chock University Hassan II, Casablanca, MoroccoDepartment of Mathematics, Laboratory of Topology, Algebra, Geometry, and Discrete Mathematics, Faculty of Sciences Aïn Chock University Hassan II, Casablanca, MoroccoDepartment of Mathematics, Laboratory of Topology, Algebra, Geometry, and Discrete Mathematics, Faculty of Sciences Aïn Chock University Hassan II, Casablanca, MoroccoIn 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.http://dx.doi.org/10.1155/2021/6547407 |
| spellingShingle | Faouaz Saadi Othman Tyr Radouan Daher Generalized Hausdorff Operators on K̇α,qβ,pℝ and HK̇α,qβ,p,Nℝ in the Dunkl Settings Journal of Function Spaces |
| title | Generalized Hausdorff Operators on K̇α,qβ,pℝ and HK̇α,qβ,p,Nℝ in the Dunkl Settings |
| title_full | Generalized Hausdorff Operators on K̇α,qβ,pℝ and HK̇α,qβ,p,Nℝ in the Dunkl Settings |
| title_fullStr | Generalized Hausdorff Operators on K̇α,qβ,pℝ and HK̇α,qβ,p,Nℝ in the Dunkl Settings |
| title_full_unstemmed | Generalized Hausdorff Operators on K̇α,qβ,pℝ and HK̇α,qβ,p,Nℝ in the Dunkl Settings |
| title_short | Generalized Hausdorff Operators on K̇α,qβ,pℝ and HK̇α,qβ,p,Nℝ in the Dunkl Settings |
| title_sort | generalized hausdorff operators on kα qβ pr and hkα qβ p nr in the dunkl settings |
| url | http://dx.doi.org/10.1155/2021/6547407 |
| work_keys_str_mv | AT faouazsaadi generalizedhausdorffoperatorsonkaqbprandhkaqbpnrinthedunklsettings AT othmantyr generalizedhausdorffoperatorsonkaqbprandhkaqbpnrinthedunklsettings AT radouandaher generalizedhausdorffoperatorsonkaqbprandhkaqbpnrinthedunklsettings |