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 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.
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