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arXiv · 2503.15291

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

Pritam Ganguly·Abhishek Ghosh
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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 $L^p$- 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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BibTeXRIS

Pritam Ganguly, Abhishek Ghosh. 2025-03-19. Dimension free estimates for the vector-valued Hardy--Littlewood maximal function on the Heisenberg group. https://arxiv.org/abs/2503.15291

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