Furstenberg set theorem for transversal families of functions
Classical Analysis and ODEs
2025-08-27 v1 Combinatorics
Abstract
We prove an extension of the Furstenberg set theorem to families of graphs satisfying a transversality condition. We apply the result to derive bounds on -norms of Fourier transforms of fractal measures supported on plane curves.
Keywords
Cite
@article{arxiv.2508.19047,
title = {Furstenberg set theorem for transversal families of functions},
author = {Tuomas Orponen and Aleksi Pyörälä and Guangzeng Yi},
journal= {arXiv preprint arXiv:2508.19047},
year = {2025}
}
Comments
80 pages, 2 figures