Hardy spaces associated with some anisotropic mixed-norm Herz spaces and their applications
In this article, we introduce anisotropic mixed-norm Herz spaces K˙q→,a→α,p(Rn){\dot{K}}_{\overrightarrow{q},\overrightarrow{a}}^{\alpha ,p}\left({{\mathbb{R}}}^{n}) and Kq→,a→α,p(Rn){K}_{\overrightarrow{q},\overrightarrow{a}}^{\alpha ,p}\left({{\mathbb{R}}}^{n}) and investigate some basic propertie...
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| Format: | Article |
| Language: | English |
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De Gruyter
2023-09-01
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| Series: | Open Mathematics |
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| Online Access: | https://doi.org/10.1515/math-2022-0599 |
| _version_ | 1797693198112391168 |
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| author | Zhao Yichun Zhou Jiang |
| author_facet | Zhao Yichun Zhou Jiang |
| author_sort | Zhao Yichun |
| collection | DOAJ |
| description | In this article, we introduce anisotropic mixed-norm Herz spaces K˙q→,a→α,p(Rn){\dot{K}}_{\overrightarrow{q},\overrightarrow{a}}^{\alpha ,p}\left({{\mathbb{R}}}^{n}) and Kq→,a→α,p(Rn){K}_{\overrightarrow{q},\overrightarrow{a}}^{\alpha ,p}\left({{\mathbb{R}}}^{n}) and investigate some basic properties of those spaces. Furthermore, we establish the Rubio de Francia extrapolation theory, which resolves the boundedness problems of Calderón-Zygmund operators and fractional integral operator and their commutators, on spaces K˙q→,a→α,p(Rn){\dot{K}}_{\overrightarrow{q},\overrightarrow{a}}^{\alpha ,p}\left({{\mathbb{R}}}^{n}) and Kq→,a→α,p(Rn){K}_{\overrightarrow{q},\overrightarrow{a}}^{\alpha ,p}\left({{\mathbb{R}}}^{n}). Especially, the Littlewood-Paley characterizations of anisotropic mixed-norm Herz spaces are also gained. As the generalization of anisotropic mixed-norm Herz spaces, we introduce anisotropic mixed-norm Herz-Hardy spaces HK˙q→,a→α,p(Rn)H{\dot{K}}_{\overrightarrow{q},\overrightarrow{a}}^{\alpha ,p}\left({{\mathbb{R}}}^{n}) and HKq→,a→α,p(Rn)H{K}_{\overrightarrow{q},\overrightarrow{a}}^{\alpha ,p}\left({{\mathbb{R}}}^{n}), on which atomic decomposition and molecular decomposition are obtained. Moreover, we gain the boundedness of classical Calderón-Zygmund operators. |
| first_indexed | 2024-03-12T02:40:06Z |
| format | Article |
| id | doaj.art-402ba6769c0d47b78b6a7ebba655aaab |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-03-12T02:40:06Z |
| publishDate | 2023-09-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-402ba6769c0d47b78b6a7ebba655aaab2023-09-04T07:10:00ZengDe GruyterOpen Mathematics2391-54552023-09-0121113210.1515/math-2022-0599Hardy spaces associated with some anisotropic mixed-norm Herz spaces and their applicationsZhao Yichun0Zhou Jiang1College of Mathematics and System Science, Xinjiang University, Urumqi, 830046, P.R. ChinaCollege of Mathematics and System Science, Xinjiang University, Urumqi, 830046, P.R. ChinaIn this article, we introduce anisotropic mixed-norm Herz spaces K˙q→,a→α,p(Rn){\dot{K}}_{\overrightarrow{q},\overrightarrow{a}}^{\alpha ,p}\left({{\mathbb{R}}}^{n}) and Kq→,a→α,p(Rn){K}_{\overrightarrow{q},\overrightarrow{a}}^{\alpha ,p}\left({{\mathbb{R}}}^{n}) and investigate some basic properties of those spaces. Furthermore, we establish the Rubio de Francia extrapolation theory, which resolves the boundedness problems of Calderón-Zygmund operators and fractional integral operator and their commutators, on spaces K˙q→,a→α,p(Rn){\dot{K}}_{\overrightarrow{q},\overrightarrow{a}}^{\alpha ,p}\left({{\mathbb{R}}}^{n}) and Kq→,a→α,p(Rn){K}_{\overrightarrow{q},\overrightarrow{a}}^{\alpha ,p}\left({{\mathbb{R}}}^{n}). Especially, the Littlewood-Paley characterizations of anisotropic mixed-norm Herz spaces are also gained. As the generalization of anisotropic mixed-norm Herz spaces, we introduce anisotropic mixed-norm Herz-Hardy spaces HK˙q→,a→α,p(Rn)H{\dot{K}}_{\overrightarrow{q},\overrightarrow{a}}^{\alpha ,p}\left({{\mathbb{R}}}^{n}) and HKq→,a→α,p(Rn)H{K}_{\overrightarrow{q},\overrightarrow{a}}^{\alpha ,p}\left({{\mathbb{R}}}^{n}), on which atomic decomposition and molecular decomposition are obtained. Moreover, we gain the boundedness of classical Calderón-Zygmund operators.https://doi.org/10.1515/math-2022-0599anisotropicmixed-normherz spaceherz-hardy spaceshardy-littlewood maximal operator42b3542b2542b20 |
| spellingShingle | Zhao Yichun Zhou Jiang Hardy spaces associated with some anisotropic mixed-norm Herz spaces and their applications Open Mathematics anisotropic mixed-norm herz space herz-hardy spaces hardy-littlewood maximal operator 42b35 42b25 42b20 |
| title | Hardy spaces associated with some anisotropic mixed-norm Herz spaces and their applications |
| title_full | Hardy spaces associated with some anisotropic mixed-norm Herz spaces and their applications |
| title_fullStr | Hardy spaces associated with some anisotropic mixed-norm Herz spaces and their applications |
| title_full_unstemmed | Hardy spaces associated with some anisotropic mixed-norm Herz spaces and their applications |
| title_short | Hardy spaces associated with some anisotropic mixed-norm Herz spaces and their applications |
| title_sort | hardy spaces associated with some anisotropic mixed norm herz spaces and their applications |
| topic | anisotropic mixed-norm herz space herz-hardy spaces hardy-littlewood maximal operator 42b35 42b25 42b20 |
| url | https://doi.org/10.1515/math-2022-0599 |
| work_keys_str_mv | AT zhaoyichun hardyspacesassociatedwithsomeanisotropicmixednormherzspacesandtheirapplications AT zhoujiang hardyspacesassociatedwithsomeanisotropicmixednormherzspacesandtheirapplications |