| Bilinear Strongly Singular Calder\'{o}n-Zygmund Operators and Their Commutators on Non-Homogeneous Generalized Morrey Spaces |
| Received:January 31, 2023 Revised:June 01, 2023 |
| Key Words:
non-homogeneous metric measure space bilinear strongly singular Calder\'{o}n-Zygmund operator commutator space $\widetilde{\mathrm{RBMO}}(\mu)$ generalized Morrey space
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.12201500), the Science Foundation for Youths of Gansu Province (Grant No.22JR5RA173) and the Young Teachers' Scientific Research Ability Promotion Project of Northwest Normal University (Grant No.NWNU-LKQN2020-07). |
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| Abstract: |
| The main goal of this paper is to establish the boundedness of bilinear strongly singular operator $\widetilde{T}$ and its commutator $\widetilde{T}_{b_{1},b_{2}}$ on generalized Morrey spaces $M^{u}_{p}(\mu)$ over non-homogeneous metric measure spaces. Under assumption that the Lebesgue measurable functions $u, u_{1}$ and $u_{2}$ belong to $\mathbb{W}_{\tau}$ for $\tau\in(0,2)$, and $u_{1}u_{2}=u$. The authors prove that $\widetilde{T}$ is bounded from product spaces $M^{u_{1}}_{p_{1}}(\mu)\times M^{u_{2}}_{p_{2}}(\mu)$ into spaces $M^{u}_{p}(\mu)$, where $\frac{1}{p}=\frac{1}{p_{1}}+\frac{1}{p_{2}}$ with $1 |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2024.01.006 |
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