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

Abstract

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 $\mathbb{H}^n$ 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 $L^{p}(\mathbb{H}^n) \times L^{q}(\mathbb{H}^n)$ spaces, for $n \geq 2$. For the full maximal functions, we obtain optimal range except possibly at the end points.