English

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 LpL^{p}-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