Bounded estimates for maximal functions over hypersurfaces in $\mathbb{R}^3$-China University of Mining & Technology-Beijing-China University of Mining & Technology-Beijing

Bounded estimates for maximal functions over hypersurfaces in $\mathbb{R}^3$

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speaker: Wenjuan Li, Northwestern Polytechnical University, Professor

time: 2024.4.26，3:00 PM

place: Yifu Building 1537

Abstract:

In this article, we study maximal functions related to hypersurfaces with vanishing Gaussian curvature in $\mathbb{R}^3$. Firstly, we characterize the $L^p\rightarrow L^q$ boundedness of local maximal operators along homogeneous hypersurfaces. Moreover, weighted $L^p$-estimates are obtained for the corresponding global operators. Secondly, for a class of hypersurfaces that lack a homogeneous structure and pass through the origin, we attempt to look for other geometric properties instead of height of hypersurfaces to characterize the optimal $L^p$-boundedness of the corresponding global maximal operators.

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​Bounded estimates for maximal functions over hypersurfaces in $\mathbb{R}^3$

Bounded estimates for maximal functions over hypersurfaces in $\mathbb{R}^3$