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

We prove an almost everywhere convergence result for Bochner–Riesz means of (Formula presented.) functions on Heisenberg-type groups, yielding the existence of a (Formula presented.) for which convergence holds for means of arbitrarily small order. The proof hinges on a reduction of weighted (Formula presented.) 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.