Composition of rough singular integral operators on rearrangement invariant Banach type spaces
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910361447301120 |
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| author | Tan, Jiawei Xue, Qingying |
| author_facet | Tan, Jiawei Xue, Qingying |
| contents | Let $Ω$ be a homogeneous function of degree zero and enjoy the vanishing condition on the unit sphere $\mathbb{S}^{n-1}(n\geq 2)$. Let $T_Ω$ be the convolution singular integral operator with kernel ${Ω(x)}{|x|^{-n}}$. In this paper, when $Ω\in L^{\infty}(\mathbb {S}^{n-1})$, we consider the quantitative weighted bounds of the composite operators of $T_Ω$ on rearrangement invariant Banach function spaces. These spaces contain the classical Lorentz spaces and Orlicz spaces as special examples. Weighted boundedness of the composite operators on rearrangement invariant quasi-Banach spaces were also given. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_05840 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Composition of rough singular integral operators on rearrangement invariant Banach type spaces Tan, Jiawei Xue, Qingying Classical Analysis and ODEs 42B20 Let $Ω$ be a homogeneous function of degree zero and enjoy the vanishing condition on the unit sphere $\mathbb{S}^{n-1}(n\geq 2)$. Let $T_Ω$ be the convolution singular integral operator with kernel ${Ω(x)}{|x|^{-n}}$. In this paper, when $Ω\in L^{\infty}(\mathbb {S}^{n-1})$, we consider the quantitative weighted bounds of the composite operators of $T_Ω$ on rearrangement invariant Banach function spaces. These spaces contain the classical Lorentz spaces and Orlicz spaces as special examples. Weighted boundedness of the composite operators on rearrangement invariant quasi-Banach spaces were also given. |
| title | Composition of rough singular integral operators on rearrangement invariant Banach type spaces |
| topic | Classical Analysis and ODEs 42B20 |
| url | https://arxiv.org/abs/2403.05840 |