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Commutators of Fractional Maximal Functions with $\widetilde{\mathrm{RBMO}}(\mu)$ on Orlicz Spaces over Non-homogeneous Metric Spaces |
Commutators of fractional maximal functions on Orlicz spaces over non-homogeneous metric spaces |
Received:November 21, 2023 Revised:June 13, 2024 |
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中文关键词: |
英文关键词:Non-homogeneous metric measure space fractional Maximal function commutator space $\widetilde{\mathrm{RBMO}}(\mu)$ Orlicz space |
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中文摘要: |
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英文摘要: |
Let $(\mathcal{X},d,\mu)$ be a non-homogeneous metric measure space satisfying the geometrically doubling and the upper doubling conditions in the sense of Hyt\"{o}nen. In this setting, the authors prove that the commutator $M^{(\alpha)}_{b}$ formed by $b\in\widetilde{\mathrm{RBMO}}(\mu)$ and the fractional maximal function $M^{(\alpha)}$ is bounded from
Lebesgue spaces $L^{p}(\mu)$ into spaces $L^{q}(\mu)$, where $\frac{1}{q}=\frac{1}{p}-\alpha$ for $\alpha\in(0,1)$
and $p\in(1,\frac{1}{\alpha})$. Furthermore, the boundedness of the $M^{(\alpha)}_{b}$ on Orlicz spaces $L^{\Phi}(\mu)$
is established. |
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