On $L^{p}$-improving bounds for maximal operators associated with curves of finite type in the plane

Wenjuan Li, Huiju Wang

Published 2023-03-06, updated 2023-05-10Version 2

In this paper, we study the $L^{p}$-improving property for the local maximal operators along a large class of curves of finite type in the plane with dilation set $E \subset [1,2]$. The $L^{p}$-improving region depends on the order of finite type and the fractal dimension of $E$. In particular, various impacts of non-isotropic dilations are also deeply considered.