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This article establishes dimension-free fefferman-stein inequalities for the Hardy-Littlewood maximal function, indicating implications for UMD lattices.
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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Ganguly et al. (2025) studied this question.
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