Bilinear Korányi spherical maximal function on the Heisenberg group

Abstract

We introduce the bilinear Korányi spherical means on the Heisenberg group $\mathbb{H}^n,$ and derive $L^{p_1}(\mathbb{H}^n) \times L^{p_2}(\mathbb{H}^n) \to L^{p}(\mathbb{H}^n)$ estimates for the associated bilinear Korányi spherical maximal function on $\mathbb{H}^n.$ We also address multilinear extensions of our results.