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Dimension-free estimates for the Hardy--Littlewood maximal operator made their debut in the seminal work of Stein and Str\"{o}mberg in the 1980s. Their breakthrough introduced a new perspective in harmonic analysis, highlighting the importance of obtaining bounds that are independent of the ambient dimension. Since then, such estimates have become a central focus in the field, owing to their strength, generality, and applicability in both Euclidean and non-Euclidean settings.
In this talk, we will discuss dimension-free estimates for the vector-valued Hardy--Littlewood maximal operator associated with averages over Kor\'{a}nyi balls in the Heisenberg group. A key ingredient in our approach is the establishment of $L^p$ bounds for vector-valued Nevo--Thangavelu spherical maximal functions, which play a crucial role in our analysis.
This is joint work with Abhishek Ghosh. |