## Abstract

The aim of this paper is to establish the boundedness of the commutator [*b*_{1}, *b*_{2}, *T*_{θ}], which generated by the bilinear *θ*-type Calderón–Zygmund operators *T*_{θ} and the functions \(b_1, b_2 \in \widetilde {RBMO}(\mu)\), on non-homogeneous metric measure space satisfying the so-called geometrically doubling and the upper doubling conditions. Under the assumption that the dominating function λ satisfies the *ε*-weak reverse doubling conditions, the author proves that the commutator [*b*_{1}, *b*_{2}, *T*_{θ}] is bounded from the Lebesgue space *L*^{p}(*μ*) into the product of Lebesgue space \({L^{{p_1}}}(\mu ) \times {L^{{p_2}}}(\mu )\) with \(\frac{1}{p} = \frac{1}{{{p_1}}} + \frac{1}{{{p_2}}}(1 < p,{p_1},{p_2} < \infty )\). Furthermore, the boundedness of the commutator [*b*_{1}, *b*_{2}, *T*_{θ}] on Morrey space \(M_p^q(\mu)\) is also obtained, where 1 < *q* ≤ *p* < ∞.

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## Additional information

This research was supported by the Doctoral Scientific Research Foundation of Northwest Normal University (No. 0002020203).

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### Cite this article

Lu, G. Commutators of Bilinear *θ*-Type Calderón–Zygmund Operators on Morrey Spaces Over Non-Homogeneous Spaces.
*Anal Math* **46, **97–118 (2020). https://doi.org/10.1007/s10476-020-0020-3

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### Key words and phrases

- non-homogeneous metric measure space
- commutator
- bilinear
*θ*-type Calderón–Zygmund operator - \(\widetilde {RBMO}(\mu)\)
- Morrey space

### Mathematics Subject Classification

- primary 42B20
- secondary 46E30
- 42B35
- 30L99