The aim of this paper is to establish the boundedness of the commutator [b1, b2, Tθ], which generated by the bilinear θ-type Calderon–Zygmund operators Tθ 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 e-weak reverse doubling conditions, the author proves that the commutator [b1, b2, Tθ] is bounded from the Lebesgue space Lp(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 [b1, b2, Tθ] on Morrey space $$M_p^q(\mu)$$ is also obtained, where 1 < q ≤ p < ∞.

中文翻译：

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非齐次空间上莫雷空间上双线性 θ 型 Calderón-Zygmund 算子的换向器

本文的目的是建立由双线性 θ 型 Calderon-Zygmund 算子 Tθ 和函数 $$b_1, b_2 \in \widetilde {RBMO}( \mu)$$，在满足所谓几何加倍和上加倍条件的非齐次度量空间上。在支配函数λ满足e-weak反向加倍条件的假设下，作者证明了交换子[b1, b2, Tθ]从勒贝格空间Lp(μ)有界到勒贝格空间$${L ^{{p_1}}}(\mu ) \times {L^{{p_2}}}(\mu )$$ 与 $$\frac{1}{p} = \frac{1}{{{p_1} }} + \frac{1}{{{p_2}}}(1 < p,{p_1},{p_2} < \infty )$$。此外，还获得了Morrey 空间$$M_p^q(\mu)$$ 上交换子[b1, b2, Tθ] 的有界性，其中1 < q ≤ p < ∞。