We establish the weighted estimates for the parametric Marcinkiewicz integral operators with rough kernels along “polynomial curves” on \(\mathbb {R}^n\). As applications, we obtain that the above operators are bounded on the mixed radial-angular spaces, on the vector-valued mixed radial-angular spaces and on the vector-valued function spaces. Particularly, the above bounds are independent of the coefficients of the polynomials in the definition of the operators.

中文翻译：

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Marcinkiewicz积分的加权估计及其在角积分中的应用

我们沿着\（\ mathbb {R} ^ n \）上的“多项式曲线”，对具有粗糙核的参数Marcinkiewicz积分算子建立加权估计。作为应用，我们获得了上述算子在混合径向角空间，矢量值混合径向角空间和矢量值函数空间上有界。特别地，在运算符的定义中，上述界限与多项式的系数无关。