Commutators of multilinear $ \theta $-type generalized fractional integrals on non-homogeneous metric measure spaces

Xiangxing Tao; Jiahui Wang; Xiangxing Tao; Jiahui Wang

doi:10.3934/math.2022535

AIMS Mathematics

2022, Volume 7, Issue 6: 9627-9647. doi: 10.3934/math.2022535

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Research article

Commutators of multilinear $ \theta $-type generalized fractional integrals on non-homogeneous metric measure spaces

Xiangxing Tao ,
Jiahui Wang ^,

Department of Mathematics, School of Science, Zhejiang University of Science and Technology, Hangzhou 310023, China

Received: 23 November 2021 Revised: 28 February 2022 Accepted: 02 March 2022 Published: 15 March 2022
MSC : 42B35, 47B37, 28A35

Let $ {\mathcal{I}_{\alpha, m}} $ be the multilinear $ \theta $-type generalized fractional integrals and $ \vec{b}_{\sigma} $ be the vector with each $ b_{\sigma_{i}} \in \widetilde{{\rm{RBMO}}}\left(\mu\right) $. The boundedness for $ {\mathcal{I}_{\alpha, m}} $ and the iterated multi-commutators $ {\mathcal{I}_{\alpha, m, \vec{b}_\sigma}} $ on Lebesgue spaces over non-homogeneous spaces are showed in this paper.
- multilinear $ \theta $-type generalized fractional integrals,
- iterated commutators,
- non-homogeneous measures,
- boundedness,
- Lebesgue spaces
Citation: Xiangxing Tao, Jiahui Wang. Commutators of multilinear $ \theta $-type generalized fractional integrals on non-homogeneous metric measure spaces[J]. AIMS Mathematics, 2022, 7(6): 9627-9647. doi: 10.3934/math.2022535

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Abstract

Let $ {\mathcal{I}_{\alpha, m}} $ be the multilinear $ \theta $-type generalized fractional integrals and $ \vec{b}_{\sigma} $ be the vector with each $ b_{\sigma_{i}} \in \widetilde{{\rm{RBMO}}}\left(\mu\right) $. The boundedness for $ {\mathcal{I}_{\alpha, m}} $ and the iterated multi-commutators $ {\mathcal{I}_{\alpha, m, \vec{b}_\sigma}} $ on Lebesgue spaces over non-homogeneous spaces are showed in this paper.

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