Speaker：Wenjuan Li（Northwestern Polytechnical University）

Time：2022-09-16, 14:30

Location：Tencent Meeting ID：279-804-861（No Password）

Abstract:

In this paper, we establish weighted estimates for a wide class of maximal functions along some finite type curves and hypersurfaces. In particular, various impacts of non-isotropic dilations are considered. Via the methodology of sparse domination, the weighted estimates for the global maximal functions can be reduced to the $L^{p}$-improving properties of the corresponding localized maximal functions. We mainly focus on proving the $L^{p}\rightarrow L^{q}$ bounds $(q >p)$ for localized maximal functions with non-isotropic dilations of curves and hypersurfaces whose curvatures vanish to finite order at some points. This is a joint work with Dr. Huiju Wang and Dr. Yujia Zhai.