We prove that a variety of oscillatory and polynomial Carleson operators are uniformly bounded on the family of parameters under considerations. As a particular application of our techniques, we prove uniform bounds for oscillatory Carleson operators near a single scale version of the quadratic Carleson operator.

中文翻译：

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振荡和多项式Carleson算子的一致界

我们证明，考虑时，各种振荡和多项式Carleson算子均统一约束在参数族上。作为我们技术的一种特殊应用，我们证明了振荡Carleson算子的统一界线接近于二次Carleson算子的单比例版本。