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October 8, 2025Open Access

Dimension free estimates for the vector-valued Hardy--Littlewood maximal function on the Heisenberg group

Key Points

Dimension-free fefferman-stein inequalities indicate significant results for the hard-littlewood maximal function.
The $L^p$-boundedness of the vector-valued nevo-thangavelu spherical maximal function plays a key role in proofs.
Generalization to more complex umd lattices broadens the scope of the initial findings.
This work enhances the understanding of maximal functions in the context of the heisenberg group.

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 Lᵖ- boundedness of the vector-valued Nevo-Thangavelu spherical maximal function, which plays a crucial role in our proofs of the main theorems.

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Cite This Study

Ganguly et al. (Wed,) studied this question.

synapsesocial.com/papers/68e62de1a8c0c6d4587400d6 https://doi.org/https://doi.org/10.48550/arxiv.2503.15291

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