Uniform volume estimates and maximal functions on generalized Heisenberg-type groups
Classical Analysis and ODEs
2026-04-17 v1 Analysis of PDEs
Abstract
On generalized Heisenberg-type groups , we give uniform volume estimates for the ball defined by a large class of Carnot-Carath\'{e}odory distances, and establish weak (1, 1) -estimates for associated centered Hardy-Littlewood maximal functions, extending the results in \cite{BLZ25}. As a by-product, we establish uniformly volume doubling property on Heisenberg groups for a class of left-invariant Riemannian metrics.
Cite
@article{arxiv.2604.14715,
title = {Uniform volume estimates and maximal functions on generalized Heisenberg-type groups},
author = {Cheng Bi and Hong-Quan Li},
journal= {arXiv preprint arXiv:2604.14715},
year = {2026}
}
Comments
22 pages, incporporating suggestions from referees reports, accepted for publication in Adv. Nonlinear Stud., Special Issue in honor of Professor Leonard Gross's 95th birthday