Necessary and sufficient conditions for boundedness of commutators of fractional integral operators on slice spaces
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916470200467456 |
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| author | Yang, Heng Zhou, Jiang |
| author_facet | Yang, Heng Zhou, Jiang |
| contents | Let $0<t<\infty$, $0<α<n$, $1<p<r<\infty$ and $1<q<s<\infty$. In this paper, we prove that $b\in B M O\left(\mathbb{R}^{n}\right)$ if and only if the commutator $[b, T_{Ω,α}]$ generated by the fractional integral operator with the rough kernel $T_{Ω,α}$ and the locally integrable function $b$ is bounded from the slice space $(E_{p}^{q})_{t}(\mathbb{R}^{n})$ to $(E_{r}^{s})_{t}(\mathbb{R}^{n})$. Meanwhile, we also show that $b\in Lip_β(\mathbb{R}^{n}) $($0<β<1)$ if and only if the commutator $\left[b, T_{Ω,α}\right]$ is bounded from $(E_{p}^{q})_{t}(\mathbb{R}^{n})$ to $(E_{r}^{s})_{t}(\mathbb{R}^{n})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_03830 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Necessary and sufficient conditions for boundedness of commutators of fractional integral operators on slice spaces Yang, Heng Zhou, Jiang Functional Analysis Let $0<t<\infty$, $0<α<n$, $1<p<r<\infty$ and $1<q<s<\infty$. In this paper, we prove that $b\in B M O\left(\mathbb{R}^{n}\right)$ if and only if the commutator $[b, T_{Ω,α}]$ generated by the fractional integral operator with the rough kernel $T_{Ω,α}$ and the locally integrable function $b$ is bounded from the slice space $(E_{p}^{q})_{t}(\mathbb{R}^{n})$ to $(E_{r}^{s})_{t}(\mathbb{R}^{n})$. Meanwhile, we also show that $b\in Lip_β(\mathbb{R}^{n}) $($0<β<1)$ if and only if the commutator $\left[b, T_{Ω,α}\right]$ is bounded from $(E_{p}^{q})_{t}(\mathbb{R}^{n})$ to $(E_{r}^{s})_{t}(\mathbb{R}^{n})$. |
| title | Necessary and sufficient conditions for boundedness of commutators of fractional integral operators on slice spaces |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2411.03830 |