Real-variable Theory of Anisotropic Musielak-Orlicz-Lorentz Hardy Spaces with Applications to Calderón-Zygmund Operators
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arXiv
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| Natura: | Preprint |
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2024
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| _version_ | 1866915304413593600 |
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| author | Liu, Xiong Wang, Wenhua |
| author_facet | Liu, Xiong Wang, Wenhua |
| contents | Let $φ: \mathbb{R}^{n}\times[0,\infty)\rightarrow[0,\infty)$ be a Musielak-Orlicz function satisfying the uniformly anisotropic Muckenhoupt condition and be of uniformly lower type $p^-_φ$ and of uniformly upper type $p^+_φ$ with $0<p^-_φ\leq p^+_φ<\infty$, $q\in(0,\infty]$, and $A$ be a general expansive matrix on $\mathbb{R}^{n}$. In this article, the authors first introduce the anisotropic Musielak-Orlicz-Lorentz Hardy space $H^{φ,q}_A(\mathbb{R}^{n})$ which, when $q=\infty$, coincides with the known anisotropic weak Musielak-Orlicz Hardy space $H^{φ,\infty}_A(\mathbb{R}^{n})$, and then establish atomic and molecular characterizations of $H^{φ,q}_A(\mathbb{R}^{n})$. As applications, the authors prove the boundedness of anisotropic Calderón-Zygmund operators on $H^{φ,q}_A(\mathbb{R}^{n})$ when $q\in(0,\infty)$ or from the anisotropic Musielak-Orlicz Hardy space $H^φ_A(\mathbb{R}^{n})$ to $H^{φ,\infty}_A(\mathbb{R}^{n})$ in the critical case. The ranges of all the exponents under consideration are the best possible admissible ones which particularly improve all the known corresponding results for $H^{φ,\infty}_A(\mathbb{R}^{n})$ via widening the original assumption $0<p^-_φ\leq p^+_φ\leq1$ into the full range $0<p^-_φ\leq p^+_φ<\infty$, and all the results when $q\in(0,\infty)$ are new and generalized from isotropic setting to anisotropic setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_06611 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Real-variable Theory of Anisotropic Musielak-Orlicz-Lorentz Hardy Spaces with Applications to Calderón-Zygmund Operators Liu, Xiong Wang, Wenhua Classical Analysis and ODEs Functional Analysis Primary 42B35, Secondary 42B30, 35J25, 42B37, 42B25 Let $φ: \mathbb{R}^{n}\times[0,\infty)\rightarrow[0,\infty)$ be a Musielak-Orlicz function satisfying the uniformly anisotropic Muckenhoupt condition and be of uniformly lower type $p^-_φ$ and of uniformly upper type $p^+_φ$ with $0<p^-_φ\leq p^+_φ<\infty$, $q\in(0,\infty]$, and $A$ be a general expansive matrix on $\mathbb{R}^{n}$. In this article, the authors first introduce the anisotropic Musielak-Orlicz-Lorentz Hardy space $H^{φ,q}_A(\mathbb{R}^{n})$ which, when $q=\infty$, coincides with the known anisotropic weak Musielak-Orlicz Hardy space $H^{φ,\infty}_A(\mathbb{R}^{n})$, and then establish atomic and molecular characterizations of $H^{φ,q}_A(\mathbb{R}^{n})$. As applications, the authors prove the boundedness of anisotropic Calderón-Zygmund operators on $H^{φ,q}_A(\mathbb{R}^{n})$ when $q\in(0,\infty)$ or from the anisotropic Musielak-Orlicz Hardy space $H^φ_A(\mathbb{R}^{n})$ to $H^{φ,\infty}_A(\mathbb{R}^{n})$ in the critical case. The ranges of all the exponents under consideration are the best possible admissible ones which particularly improve all the known corresponding results for $H^{φ,\infty}_A(\mathbb{R}^{n})$ via widening the original assumption $0<p^-_φ\leq p^+_φ\leq1$ into the full range $0<p^-_φ\leq p^+_φ<\infty$, and all the results when $q\in(0,\infty)$ are new and generalized from isotropic setting to anisotropic setting. |
| title | Real-variable Theory of Anisotropic Musielak-Orlicz-Lorentz Hardy Spaces with Applications to Calderón-Zygmund Operators |
| topic | Classical Analysis and ODEs Functional Analysis Primary 42B35, Secondary 42B30, 35J25, 42B37, 42B25 |
| url | https://arxiv.org/abs/2410.06611 |