Maximal functions associated with families of homogeneous curves: Lp bounds for P ≤ 2,Proceedings of the Edinburgh Mathematical Society

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Maximal functions associated with families of homogeneous curves: Lp bounds for P ≤ 2
Proceedings of the Edinburgh Mathematical Society ( IF 0.7 ) Pub Date : 2020-02-03 , DOI: 10.1017/s0013091519000439
Shaoming Guo , Joris Roos , Andreas Seeger , Po-Lam Yung

Let M(u), H(u) be the maximal operator and Hilbert transform along the parabola (t, ut2). For U ⊂ (0, ∞) we consider Lp estimates for the maximal functions sup u∈U|M(u)f| and sup u∈U|H(u)f|, when 1 < p ≤ 2. The parabolas can be replaced by more general non-flat homogeneous curves.

中文翻译：

与齐次曲线族相关的最大函数：P ≤ 2 的 Lp 界限

让米(你),H(你)是最大算子和沿抛物线的希尔伯特变换 (吨,ut2）。为了ü⊂ (0, ∞) 我们考虑大号p最大函数 sup 的估计你∈ü|米(你)F| 和支持你∈ü|H(你)F|，当 1 <p≤ 2. 抛物线可以用更一般的非平坦齐次曲线代替。

更新日期：2020-02-03

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