Anisotropic interpolation theorems of Musielak-Orlicz type
Abstract Anisotropy is a common attribute of Nature, which shows different characterizations in different directions of all or part of the physical or chemical properties of an object. The anisotropic property, in mathematics, can be expressed by a fairly general discrete group of dilations { A k :...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2016-10-01
|
| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-016-1184-z |
| _version_ | 1818972263341359104 |
|---|---|
| author | Jinxia Li Ruirui Sun Baode Li |
| author_facet | Jinxia Li Ruirui Sun Baode Li |
| author_sort | Jinxia Li |
| collection | DOAJ |
| description | Abstract Anisotropy is a common attribute of Nature, which shows different characterizations in different directions of all or part of the physical or chemical properties of an object. The anisotropic property, in mathematics, can be expressed by a fairly general discrete group of dilations { A k : k ∈ Z } $\{A^{k}: k\in\mathbb{Z}\}$ , where A is a real n × n $n\times n$ matrix with all its eigenvalues λ satisfy | λ | > 1 $|\lambda|>1$ . Let φ : R n × [ 0 , ∞ ) → [ 0 , ∞ ) $\varphi: \mathbb{R}^{n}\times[0, \infty)\to[0,\infty)$ be an anisotropic Musielak-Orlicz function such that φ ( x , ⋅ ) $\varphi(x,\cdot)$ is an Orlicz function and φ ( ⋅ , t ) $\varphi(\cdot,t)$ is a Muckenhoupt A ∞ ( A ) $\mathbb {A}_{\infty}(A)$ weight. The aim of this article is to obtain two anisotropic interpolation theorems of Musielak-Orlicz type, which are weighted anisotropic extension of Marcinkiewicz interpolation theorems. The above results are new even for the isotropic weighted settings. |
| first_indexed | 2024-12-20T15:05:29Z |
| format | Article |
| id | doaj.art-d6d9ca86a962423cad8f3e2bb36db951 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-20T15:05:29Z |
| publishDate | 2016-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-d6d9ca86a962423cad8f3e2bb36db9512022-12-21T19:36:31ZengSpringerOpenJournal of Inequalities and Applications1029-242X2016-10-012016112410.1186/s13660-016-1184-zAnisotropic interpolation theorems of Musielak-Orlicz typeJinxia Li0Ruirui Sun1Baode Li2College of Mathematics and System Science, Xinjiang UniversityCollege of Mathematics and System Science, Xinjiang UniversityCollege of Mathematics and System Science, Xinjiang UniversityAbstract Anisotropy is a common attribute of Nature, which shows different characterizations in different directions of all or part of the physical or chemical properties of an object. The anisotropic property, in mathematics, can be expressed by a fairly general discrete group of dilations { A k : k ∈ Z } $\{A^{k}: k\in\mathbb{Z}\}$ , where A is a real n × n $n\times n$ matrix with all its eigenvalues λ satisfy | λ | > 1 $|\lambda|>1$ . Let φ : R n × [ 0 , ∞ ) → [ 0 , ∞ ) $\varphi: \mathbb{R}^{n}\times[0, \infty)\to[0,\infty)$ be an anisotropic Musielak-Orlicz function such that φ ( x , ⋅ ) $\varphi(x,\cdot)$ is an Orlicz function and φ ( ⋅ , t ) $\varphi(\cdot,t)$ is a Muckenhoupt A ∞ ( A ) $\mathbb {A}_{\infty}(A)$ weight. The aim of this article is to obtain two anisotropic interpolation theorems of Musielak-Orlicz type, which are weighted anisotropic extension of Marcinkiewicz interpolation theorems. The above results are new even for the isotropic weighted settings.http://link.springer.com/article/10.1186/s13660-016-1184-zanisotropic expansive dilationMuckenhoupt weightMusielak-Orlicz functionweighted Hardy spaceinterpolation |
| spellingShingle | Jinxia Li Ruirui Sun Baode Li Anisotropic interpolation theorems of Musielak-Orlicz type Journal of Inequalities and Applications anisotropic expansive dilation Muckenhoupt weight Musielak-Orlicz function weighted Hardy space interpolation |
| title | Anisotropic interpolation theorems of Musielak-Orlicz type |
| title_full | Anisotropic interpolation theorems of Musielak-Orlicz type |
| title_fullStr | Anisotropic interpolation theorems of Musielak-Orlicz type |
| title_full_unstemmed | Anisotropic interpolation theorems of Musielak-Orlicz type |
| title_short | Anisotropic interpolation theorems of Musielak-Orlicz type |
| title_sort | anisotropic interpolation theorems of musielak orlicz type |
| topic | anisotropic expansive dilation Muckenhoupt weight Musielak-Orlicz function weighted Hardy space interpolation |
| url | http://link.springer.com/article/10.1186/s13660-016-1184-z |
| work_keys_str_mv | AT jinxiali anisotropicinterpolationtheoremsofmusielakorlicztype AT ruiruisun anisotropicinterpolationtheoremsofmusielakorlicztype AT baodeli anisotropicinterpolationtheoremsofmusielakorlicztype |