In this paper, we introduce certain classes of multilinear Calderón–Zygmund operators with kernels of Dini’s type. Applying the sharp method and $A_{\vec{p}}^{\infty }(\varphi )$ functions, we first establish some weighted norm inequalities for multilinear Calderón–Zygmund operators with kernels of Dini’s type, including pointwise estimates, strong type, and weak endpoint estimates. Furthermore, similar weighted norm inequalities for commutators with $\mathrm{BMO}_{\theta }(\varphi )$ functions are also obtained, but the weak endpoint estimate is of $L({\mathrm{log}}L)$ type.

中文翻译：

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具有Dini型核及其换向器的多线性Calderón–Zygmund算子的新加权范数不等式

在本文中，我们介绍了带有Dini类型核的某些类别的多线性Calderón–Zygmund算子。应用Sharp方法和$ A _ {\ vec {p}} ^ {\ infty}（\ varphi）$函数，我们首先为带有Dini类型核的多线性Calderón–Zygmund算子建立一些加权范数不等式，包括逐点估计，强类型和较弱的端点估算值。此外，对于具有$ \ mathrm {BMO} _ {\ theta}（\ varphi）$函数的换向器，也获得了相似的加权范数不等式，但弱端点估计为$ L（{\ mathrm {log}} L）$类型。