English

A measure with small support and p-summable Fourier transform

Classical Analysis and ODEs 2024-12-11 v1

Abstract

We construct a probability measure μ\mu supported on a set of zero 2d/p2d/p-Hausdorff measure such that μ^Lp(Rd)\hat{\mu}\in L_{p}(\mathbb{R}^d).

Keywords

Cite

@article{arxiv.2412.07314,
  title  = {A measure with small support and p-summable Fourier transform},
  author = {Nikita P. Dobronravov},
  journal= {arXiv preprint arXiv:2412.07314},
  year   = {2024}
}
R2 v1 2026-06-28T20:29:10.078Z