Sparse domination and $L^{p} \rightarrow L^{q}$ estimates for maximal functions associated with curvature
Classical Analysis and ODEs
2022-02-24 v2 Functional Analysis
Abstract
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 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 bounds . As a corollary, we obtain the weighted inequalities for the corresponding global maximal functions, which generalize the known unweighted estimates.
Keywords
Cite
@article{arxiv.2202.09944,
title = {Sparse domination and $L^{p} \rightarrow L^{q}$ estimates for maximal functions associated with curvature},
author = {Wenjuan Li and Huiju Wang and Yujia Zhai},
journal= {arXiv preprint arXiv:2202.09944},
year = {2022}
}