Bilinear maximal functions associated with some degenerate surfaces on the Heisenberg group

Motivated by the works of Lee--Shuin and Borges--Foster on the Euclidean space, in this article we consider bilinear averages on the Heisenberg group Hⁿ corresponding to some degenerate surfaces associated with the Korányi norm as well as Nevo--Thangavelu type averaging structures, and study the boundedness of the their full and lacunary maximal functions on various Lᵖ(Hⁿ) × Lq(Hⁿ) spaces, for n ≥ 2. For the full maximal functions, we obtain optimal range except possibly at the end points.