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

2025/03/19 by Pritam Ganguly, Abhishek Ghosh, Ganguly, Pritam +1
Mathematics · #42B25. Secondary: 22E25 #42B35 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Primary: 43A80 #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2503.15291

openalex publication_date 2025/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we establish dimension-free Fefferman-Stein inequalities for the Hardy-Littlewood maximal function associated with averages over Korányi 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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