Anisotropic Hardy Spaces of Musielak-Orlicz Type with Applications to Boundedness of Sublinear Operators
Let φ:ℝn×[0,∞)→[0,∞) be a Musielak-Orlicz function and A an expansive dilation. In this paper, the authors introduce the anisotropic Hardy space of Musielak-Orlicz type, HAφ(ℝn), via the grand maximal function. The authors then obtain some real-variable characterizations of HAφ(ℝn) in terms of the r...
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2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/306214 |
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| author | Baode Li Dachun Yang Wen Yuan |
| author_facet | Baode Li Dachun Yang Wen Yuan |
| author_sort | Baode Li |
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| description | Let φ:ℝn×[0,∞)→[0,∞) be a Musielak-Orlicz function and A an expansive dilation. In this paper, the authors introduce the anisotropic Hardy space of Musielak-Orlicz type, HAφ(ℝn), via the grand maximal function. The authors then obtain some real-variable characterizations of HAφ(ℝn) in terms of the radial, the nontangential, and the tangential maximal functions, which generalize the known results on the anisotropic Hardy space HAp(ℝn) with p∈(0,1] and are new even for its weighted variant. Finally, the authors characterize these spaces by anisotropic atomic decompositions. The authors also obtain the finite atomic decomposition characterization of HAφ(ℝn), and, as an application, the authors prove that, for a given admissible triplet (φ,q,s), if T is a sublinear operator and maps all (φ,q,s)-atoms with q<∞ (or all continuous (φ,q,s)-atoms with q=∞) into uniformly bounded elements of some quasi-Banach spaces ℬ, then T uniquely extends to a bounded sublinear operator from HAφ(ℝn) to ℬ. These results are new even for anisotropic Orlicz-Hardy spaces on ℝn. |
| format | Article |
| id | doaj-art-9bb6bbf5f6744156b6db4f724cf6a8f4 |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
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| series | The Scientific World Journal |
| spelling | doaj-art-9bb6bbf5f6744156b6db4f724cf6a8f42025-02-03T06:06:23ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/306214306214Anisotropic Hardy Spaces of Musielak-Orlicz Type with Applications to Boundedness of Sublinear OperatorsBaode Li0Dachun Yang1Wen Yuan2School of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, ChinaSchool of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, ChinaSchool of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, ChinaLet φ:ℝn×[0,∞)→[0,∞) be a Musielak-Orlicz function and A an expansive dilation. In this paper, the authors introduce the anisotropic Hardy space of Musielak-Orlicz type, HAφ(ℝn), via the grand maximal function. The authors then obtain some real-variable characterizations of HAφ(ℝn) in terms of the radial, the nontangential, and the tangential maximal functions, which generalize the known results on the anisotropic Hardy space HAp(ℝn) with p∈(0,1] and are new even for its weighted variant. Finally, the authors characterize these spaces by anisotropic atomic decompositions. The authors also obtain the finite atomic decomposition characterization of HAφ(ℝn), and, as an application, the authors prove that, for a given admissible triplet (φ,q,s), if T is a sublinear operator and maps all (φ,q,s)-atoms with q<∞ (or all continuous (φ,q,s)-atoms with q=∞) into uniformly bounded elements of some quasi-Banach spaces ℬ, then T uniquely extends to a bounded sublinear operator from HAφ(ℝn) to ℬ. These results are new even for anisotropic Orlicz-Hardy spaces on ℝn.http://dx.doi.org/10.1155/2014/306214 |
| spellingShingle | Baode Li Dachun Yang Wen Yuan Anisotropic Hardy Spaces of Musielak-Orlicz Type with Applications to Boundedness of Sublinear Operators The Scientific World Journal |
| title | Anisotropic Hardy Spaces of Musielak-Orlicz Type with Applications to Boundedness of Sublinear Operators |
| title_full | Anisotropic Hardy Spaces of Musielak-Orlicz Type with Applications to Boundedness of Sublinear Operators |
| title_fullStr | Anisotropic Hardy Spaces of Musielak-Orlicz Type with Applications to Boundedness of Sublinear Operators |
| title_full_unstemmed | Anisotropic Hardy Spaces of Musielak-Orlicz Type with Applications to Boundedness of Sublinear Operators |
| title_short | Anisotropic Hardy Spaces of Musielak-Orlicz Type with Applications to Boundedness of Sublinear Operators |
| title_sort | anisotropic hardy spaces of musielak orlicz type with applications to boundedness of sublinear operators |
| url | http://dx.doi.org/10.1155/2014/306214 |
| work_keys_str_mv | AT baodeli anisotropichardyspacesofmusielakorlicztypewithapplicationstoboundednessofsublinearoperators AT dachunyang anisotropichardyspacesofmusielakorlicztypewithapplicationstoboundednessofsublinearoperators AT wenyuan anisotropichardyspacesofmusielakorlicztypewithapplicationstoboundednessofsublinearoperators |