The main purpose of this paper is to establish the boundedness of bilinear $$\theta $$ -type Calderon–Zygmund operator $$T_{\theta }$$ and its commutator $$[b_{1},b_{2},T_{\theta }]$$ generated by the function $$b_{i}\in \widetilde{\mathrm {RBMO}}(\mu )$$ with $$i=1,2$$ and $$T_{\theta }$$ on weighted Morrey space $$L^{p,\kappa ,\varrho }(\omega )$$ and weighted weak Morrey space $$WL^{p,\kappa ,\varrho }(\omega )$$ over non-homogeneous metric measure space. Under assumption that $$\omega $$ satisfies weighted integral conditions, the author proves that $$T_{\theta }$$ is bounded from weighted weak Morrey space $$WL^{p,\kappa ,\varrho }(\omega )$$ into weighted Morrey space $$L^{p,\kappa ,\varrho }(\omega )$$ with $$1\le p<\infty $$ . In addition, via the sharp maximal function, the boundedness of the commutator $$[b_{1},b_{2},T_{\theta }]$$ on the weighted Morrey space $$L^{p,\kappa ,\varrho }(\omega )$$ is also obtained.

中文翻译：

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非齐次加权莫雷空间上的双线性 $$\theta $$ 型 Calderón–Zygmund 算子及其交换子

本文的主要目的是建立双线性$$\theta $$ -type Calderon–Zygmund算子$$T_{\theta }$$及其换向子$$[b_{1},b_{2}, T_{\theta }]$$ 由函数 $$b_{i}\in \widetilde{\mathrm {RBMO}}(\mu )$$ 生成，其中 $$i=1,2$$ 和 $$T_{ \theta }$$ 在加权莫雷空间 $$L^{p,\kappa ,\varrho }(\omega )$$ 和加权弱莫雷空间 $$WL^{p,\kappa ,\varrho }(\omega ) $$ 在非同质度量度量空间上。在$$\omega $$满足加权积分条件的假设下，作者证明$T_{\theta }$$是从加权弱莫雷空间$$WL^{p,\kappa,\varrho }(\omega )$$ 进入加权莫雷空间 $$L^{p,\kappa ,\varrho }(\omega )$$ 和 $$1\le p<\infty $$ 。此外，通过尖锐的极大函数，交换子 $$[b_{1},b_{2} 的有界性，