论文标题
稀疏支配和$ l^{p} \ rightarrow l^{q} $估计与曲率相关的最大功能
Sparse domination and $L^{p} \rightarrow L^{q}$ estimates for maximal functions associated with curvature
论文作者
论文摘要
在本文中，我们研究了一些有限型曲线和超曲面的最大功能。特别是，考虑了非各向同性扩张的各种影响。首先，我们提供了一个通用方案，使我们能够在相应的局部最大函数满足$ l^{p} $改善属性的假设下推导全局最大函数的稀疏支配界限。其次，对于具有曲线和超曲面的非异向扩张的局部最大函数，它们的曲率在某些方面消失了有限顺序，我们建立了$ l^{p} \ rightarrow l^{q} $ bounds $（q> p）$。作为推论，我们获得了相应的全局最大函数的加权不平等，从而概括了已知的未加权估计。
In this paper, we study maximal functions along some finite type curves and hypersurfaces. In particular, various impacts of non-isotropic dilations are considered. Firstly, we provide a generic scheme that allows us to deduce the sparse domination bounds for global maximal functions under the assumption that the corresponding localized maximal functions satisfy the $L^{p}$ improving properties. Secondly, for the localized maximal functions with non-isotropic dilations of curves and hypersurfaces whose curvatures vanish to finite order at some points, we establish the $L^{p}\rightarrow L^{q}$ bounds $(q >p)$. As a corollary, we obtain the weighted inequalities for the corresponding global maximal functions, which generalize the known unweighted estimates.
