Year: 2026
Type: preprint
Abstract: In this paper, we investigate weighted $L^p\rightarrow L^q$ restriction estimates for the Fourier extension operator associated with planar curves of non-vanishing curvature. More precisely, we establish estimates of the form \begin{equation} \|Ef\|_{L^q(X)}\leq C_εR^ε\|f\|_p, \end{equation} where $X$ is an $α$-dimensional set. As an application of this result, we derive a new $L^p$ decay estimate for circular means of Fourier transforms of fractal measures in $\mathbb{R}^2$. We also construct examples that give several upper bounds for the decay exponent when $p\in[1,2]$.
Source: arXiv (Cornell University)
Authors: Cao, Zhenbin, Guo, Feilong, Li, Junfeng
Institution: Dalian University of Technology
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213597628