Characterizations of a class of Musielak--Orlicz BMO spaces via commutators of Riesz potential operators
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| Format: | Preprint |
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2026
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| _version_ | 1866908776217444352 |
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| author | Han, Yanyan Huang, Hongwei Shao, Jinghan Wu, Huoxiong |
| author_facet | Han, Yanyan Huang, Hongwei Shao, Jinghan Wu, Huoxiong |
| contents | The fractional integral operators $I_α$ can be used to characterize the Musielak--Orlicz Hardy spaces. This paper shows that for $b\in \rm BMO(\mathbb R^n)$, the commutators $[b,I_α]$ generated by fractional integral operators $I_α$ with $b$ are bounded from the Musielak--Orlicz Hardy spaces $H^{φ_1}(\mathbb R^n)$ to the Musielak--Orlicz spaces $L^{φ_2}(\mathbb R^n)$ (where $1<u<\infty$ and $φ_1$, $φ_2$ are growth functions) if and only if $b\in \mathcal {BMO}_{φ_1,u}(\mathbb R^n)$, which are a class of non-trivial subspaces of $\rm BMO(\mathbb R^n)$. Additionally, we obtain the boundedness of the commutator $[b,I_α]$ from $H^{φ_1}(\mathbb R^n)$ to $H^{φ_2}(\mathbb R^n)$. The corresponding results are also provided for commutators of fractional integrals associated with general homogeneous kernels. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_13788 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Characterizations of a class of Musielak--Orlicz BMO spaces via commutators of Riesz potential operators Han, Yanyan Huang, Hongwei Shao, Jinghan Wu, Huoxiong Classical Analysis and ODEs The fractional integral operators $I_α$ can be used to characterize the Musielak--Orlicz Hardy spaces. This paper shows that for $b\in \rm BMO(\mathbb R^n)$, the commutators $[b,I_α]$ generated by fractional integral operators $I_α$ with $b$ are bounded from the Musielak--Orlicz Hardy spaces $H^{φ_1}(\mathbb R^n)$ to the Musielak--Orlicz spaces $L^{φ_2}(\mathbb R^n)$ (where $1<u<\infty$ and $φ_1$, $φ_2$ are growth functions) if and only if $b\in \mathcal {BMO}_{φ_1,u}(\mathbb R^n)$, which are a class of non-trivial subspaces of $\rm BMO(\mathbb R^n)$. Additionally, we obtain the boundedness of the commutator $[b,I_α]$ from $H^{φ_1}(\mathbb R^n)$ to $H^{φ_2}(\mathbb R^n)$. The corresponding results are also provided for commutators of fractional integrals associated with general homogeneous kernels. |
| title | Characterizations of a class of Musielak--Orlicz BMO spaces via commutators of Riesz potential operators |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2601.13788 |