论文标题
$ l^2 $估计与空间曲线相关的NikodyM最大功能
$L^2$ estimates for a Nikodym maximal function associated to space curves
论文作者
论文摘要
我们考虑$ l^p \ rightArrow l^p $界限的最大功能与$ \ mathbb {r}^{d+1} $相关的单参数管系列，其方向由非分级曲线曲线$γ$确定。这些操作员出现在对太空曲线上最大平均值的分析中。主要定理将已知的结果$ d = 2 $和$ d = 3 $作为一般尺寸。关键要素是由KO-Lee-oh的最新工作激发的入学计划。
We consider the $L^p \rightarrow L^p$ boundedness of a Nikodym maximal function associated to a one-parameter family of tubes in $\mathbb{R}^{d+1}$ whose directions are determined by a non-degenerate curve $γ$ in $\mathbb{R}^d$. These operators arise in the analysis of maximal averages over space curves. The main theorem generalises the known results for $d = 2$ and $d = 3$ to general dimensions. The key ingredient is an induction scheme motivated by recent work of Ko--Lee--Oh.
