Hilbert transforms and maximal functions along flat curves on the Heisenberg group

2024/02/16 by Zhang, Lingxiao
#42B20 #42B25 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2402.10653

Abstract

We establish the L^p boundedness of Hilbert transforms and maximal functions along flat curves in the Heisenberg group. This generalizes the ℝⁿ result by Carbery, Christ, Vance, Wainger, and Watson. What is new about our result compared to the Heisenberg group generalization by Carbery, Wainger, and Wright is that we allow all three components of the curves to vary independently, we keep the original form of the conditions required in the ℝⁿ case, and our method is likely to be generalized to other stratified nilpotent groups.

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