In this paper, we study the mixed radial-angular integrability for maximal operators related to a class of rough singular integrals along “polynomial curves". Under assuming that the kernel satisfies certain rather weak size condition on sphere, we obtain the boundedness of such maximal operators on the mixed radial-angular Lebesgue spaces. Meanwhile, on the corresponding vector-valued versions are also established.

中文翻译：

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粗糙极大值算子的混合径向角可积性

在本文中，我们研究了与一类沿“多项式曲线”的粗糙奇异积分相关的极大算子的混合径向角可积性。假设核满足球体上某些相当弱的尺寸条件，我们得到这种极大值的有界混合径向角 Lebesgue 空间上的算子。同时，还建立了相应的向量值版本。