  We prove an almost everywhere convergence result for Bochner-Riesz means of
$L^p$ 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 $L^2$ 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.
