Herz-Type Hardy Spaces Associated with Ball Quasi-Banach Function Spaces
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910992523329536 |
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| author | Wang, Aiting Wang, Wenhua Wei, Mingquan Li, Baode |
| author_facet | Wang, Aiting Wang, Wenhua Wei, Mingquan Li, Baode |
| contents | Let $X$ be a ball quasi-Banach function space, $α\in \mathbb{R}$ and $q\in(0,\infty)$. In this paper, the authors first introduce the Herz-type Hardy space $\mathcal{H\dot{K}}_{X}^{α,\,q}({\mathbb {R}}^n)$, which is defined via the non-tangential grand maximal function. Under some mild assumptions on $X$, the authors establish the atomic decompositions of $\mathcal{H\dot{K}}_{X}^{α,\,q}({\mathbb {R}}^n)$. As an application, the authors
obtain the boundedness of certain sublinear operators from $\mathcal{H\dot{K}}_{X}^{α,\,q}({\mathbb {R}}^n)$ to $\mathcal{\dot{K}}_{X}^{α,\,q}({\mathbb {R}}^n)$, where $\mathcal{\dot{K}}_{X}^{α,\,q}({\mathbb {R}}^n)$ denotes the Herz-type space associated with ball quasi-Banach function space $X$. Finally, the authors apply these results to three concrete function spaces: Herz-type Hardy spaces with variable exponent, mixed Herz-Hardy spaces and Orlicz-Herz Hardy spaces, which belong to the family of Herz-type Hardy spaces associated with ball quasi-Banach function spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_12271 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Herz-Type Hardy Spaces Associated with Ball Quasi-Banach Function Spaces Wang, Aiting Wang, Wenhua Wei, Mingquan Li, Baode Functional Analysis Classical Analysis and ODEs Primary 42B30, Secondary 42B35, 46E30 Let $X$ be a ball quasi-Banach function space, $α\in \mathbb{R}$ and $q\in(0,\infty)$. In this paper, the authors first introduce the Herz-type Hardy space $\mathcal{H\dot{K}}_{X}^{α,\,q}({\mathbb {R}}^n)$, which is defined via the non-tangential grand maximal function. Under some mild assumptions on $X$, the authors establish the atomic decompositions of $\mathcal{H\dot{K}}_{X}^{α,\,q}({\mathbb {R}}^n)$. As an application, the authors obtain the boundedness of certain sublinear operators from $\mathcal{H\dot{K}}_{X}^{α,\,q}({\mathbb {R}}^n)$ to $\mathcal{\dot{K}}_{X}^{α,\,q}({\mathbb {R}}^n)$, where $\mathcal{\dot{K}}_{X}^{α,\,q}({\mathbb {R}}^n)$ denotes the Herz-type space associated with ball quasi-Banach function space $X$. Finally, the authors apply these results to three concrete function spaces: Herz-type Hardy spaces with variable exponent, mixed Herz-Hardy spaces and Orlicz-Herz Hardy spaces, which belong to the family of Herz-type Hardy spaces associated with ball quasi-Banach function spaces. |
| title | Herz-Type Hardy Spaces Associated with Ball Quasi-Banach Function Spaces |
| topic | Functional Analysis Classical Analysis and ODEs Primary 42B30, Secondary 42B35, 46E30 |
| url | https://arxiv.org/abs/2310.12271 |