English

The circular maximal operator on Heisenberg radial functions

Classical Analysis and ODEs 2021-01-13 v2

Abstract

Lebesgue space estimates are obtained for the circular maximal function on the Heisenberg group H1\mathbb{H}^1 restricted to a class of Heisenberg radial functions. Under this assumption, the problem reduces to studying a maximal operator on the Euclidean plane. This operator has a number of interesting features: it is associated to a non-smooth curve distribution and, furthermore, fails both the usual rotational curvature and cinematic curvature conditions.

Keywords

Cite

@article{arxiv.1912.11718,
  title  = {The circular maximal operator on Heisenberg radial functions},
  author = {David Beltran and Shaoming Guo and Jonathan Hickman and Andreas Seeger},
  journal= {arXiv preprint arXiv:1912.11718},
  year   = {2021}
}

Comments

52 pages, 2 figures. Revised version incorporating referee's suggestions. To appear in Ann. Sc. Norm. Super. Pisa Cl. Sci

R2 v1 2026-06-23T12:56:30.323Z