Almost everywhere convergence of Bochner-Riesz means on Heisenberg-type groups

We prove an almost everywhere convergence result for Bochner-Riesz means of Lp functions on Heisenberg-type groups, yielding the existence of a p>2 for which convergence holds for means of arbitrarily small order. The proof hinges on a reduction of weighted L2 estimates for the maximal Bochner-Riesz operator to corresponding estimates for the non-maximal operator, and a 'dual Sobolev trace lemma', whose proof is based on refined estimates for Jacobi polynomials.