Rigidity of reflectionless Riesz measures and Sobolev estimates for Riesz transforms on Lipschitz graphs
Year: 2026
Type: preprint
Abstract: In this paper, we focus on the positive reflectionless measures rigidity problem proposed by Xavier Tolsa in [16]. Let $1\leq nn/2$, we further obtain $H^s$ estimates controlling the graph gradient and density perturbation by the normalized Riesz field under smallness of the slope and density perturbation in $L^\infty$. The constants are independent of the supports.
Source: arXiv (Cornell University)
Authors: Chen, Lu, Liu, Haolin, Liu, Hongyu
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G6591708273
OpenAlex ID: W7214719205