This paper studies the mixed radial-angular integrability of parametric Marcinkiewicz integrals along “polynomial curves”. Under the assumption that the kernels satisfy certain rather weak size conditions on the unit sphere with radial roughness, the authors prove that such operators are bounded on the mixed radial-angular spaces. Meanwhile, corresponding vector-valued versions are also obtained.

中文翻译：

---

关于具有粗糙核的 Marcinkiewicz 积分的混合径向-角可积性

本文研究了参数 Marcinkiewicz 积分沿“多项式曲线”的混合径向-角可积性。在内核满足径向粗糙度单位球体上某些相当弱的尺寸条件的假设下，作者证明了这些算子在混合径向角空间上有界。同时，也得到相应的向量值版本。