English

On exceptional sets of Hilbert transform

Classical Analysis and ODEs 2021-01-26 v1

Abstract

We prove several theorems concerning the exceptional sets of Hilbert transform on the real line. In particular, it is proved that any null set is exceptional set for the Hibert transform of an indicator function. The paper also provides a real variable approach to the Kahane-Katsnelson theorem on divergence of Fourier series.

Keywords

Cite

@article{arxiv.1611.07692,
  title  = {On exceptional sets of Hilbert transform},
  author = {Grigori Karagulyan},
  journal= {arXiv preprint arXiv:1611.07692},
  year   = {2021}
}

Comments

16 pages

R2 v1 2026-06-22T17:01:57.905Z