The Variable Muckenhoupt Weight Revisited
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910504016936960 |
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| author | Jia, Hongchao Yan, Xianjie |
| author_facet | Jia, Hongchao Yan, Xianjie |
| contents | Let $p(\cdot):\ \mathbb R^n\to(0,\infty)$ be a variable exponent function and $X$ a ball quasi-Banach function space. In this paper, we first study the relationship between two kinds of variable weights $\mathcal{W}_{p(\cdot)}(\mathbb{R}^n)$ and $A_{p(\cdot)}(\mathbb{R}^n)$. Then, by regarding the weighted variable Lebesgue space $L^{p(\cdot)}_ω(\mathbb{R}^n)$ with $ω\in\mathcal{W}_{p(\cdot)}(\mathbb{R}^n)$ as a special case of $X$ and applying known results of the Hardy-type space $H_{X}(\mathbb{R}^n)$ associated with $X$, we further obtain several equivalent characterizations of the weighted variable Hardy space $H^{p(\cdot)}_ω(\rn)$ and the boundedness of some sublinear operators on $H^{p(\cdot)}_ω(\rn)$. All of these results coincide with or improve existing ones, or are completely new. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_18947 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Variable Muckenhoupt Weight Revisited Jia, Hongchao Yan, Xianjie Classical Analysis and ODEs Functional Analysis 42B25, 42B30, 42B20, 46E30 Let $p(\cdot):\ \mathbb R^n\to(0,\infty)$ be a variable exponent function and $X$ a ball quasi-Banach function space. In this paper, we first study the relationship between two kinds of variable weights $\mathcal{W}_{p(\cdot)}(\mathbb{R}^n)$ and $A_{p(\cdot)}(\mathbb{R}^n)$. Then, by regarding the weighted variable Lebesgue space $L^{p(\cdot)}_ω(\mathbb{R}^n)$ with $ω\in\mathcal{W}_{p(\cdot)}(\mathbb{R}^n)$ as a special case of $X$ and applying known results of the Hardy-type space $H_{X}(\mathbb{R}^n)$ associated with $X$, we further obtain several equivalent characterizations of the weighted variable Hardy space $H^{p(\cdot)}_ω(\rn)$ and the boundedness of some sublinear operators on $H^{p(\cdot)}_ω(\rn)$. All of these results coincide with or improve existing ones, or are completely new. |
| title | The Variable Muckenhoupt Weight Revisited |
| topic | Classical Analysis and ODEs Functional Analysis 42B25, 42B30, 42B20, 46E30 |
| url | https://arxiv.org/abs/2406.18947 |