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arXiv · 2210.14857

$L^2$ estimates for a Nikodym maximal function associated to space curves

Aswin Govindan Sheri
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Abstract

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 $\gamma$ 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.

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Aswin Govindan Sheri. 2022-10-26. $L^2$ estimates for a Nikodym maximal function associated to space curves. https://arxiv.org/abs/2210.14857

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