Dimension free estimates for the vector-valued Hardy--Littlewood maximal function on the Heisenberg group
Classical Analysis and ODEs
2025-03-20 v1 Functional Analysis
Abstract
In this article, we establish dimension-free Fefferman-Stein inequalities for the Hardy-Littlewood maximal function associated with averages over Kor\'anyi balls in the Heisenberg group. We also generalize the result to more general UMD lattices. As a key stepping stone, we establish the - boundedness of the vector-valued Nevo-Thangavelu spherical maximal function, which plays a crucial role in our proofs of the main theorems.
Keywords
Cite
@article{arxiv.2503.15291,
title = {Dimension free estimates for the vector-valued Hardy--Littlewood maximal function on the Heisenberg group},
author = {Pritam Ganguly and Abhishek Ghosh},
journal= {arXiv preprint arXiv:2503.15291},
year = {2025}
}
Comments
22 pages