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

## TL;DR

This paper proves almost everywhere convergence of Bochner-Riesz means for L^p functions on Heisenberg-type groups, establishing convergence for some p>2 and small order means, using advanced harmonic analysis techniques.

## Contribution

It introduces a new convergence result for Bochner-Riesz means on Heisenberg-type groups, with novel reduction techniques and a dual Sobolev trace lemma.

## Key findings

- Convergence holds for some p>2 and arbitrarily small mean order.
- Reduction of weighted L^2 estimates to non-maximal operators.
- Development of a dual Sobolev trace lemma based on Jacobi polynomial estimates.

## Abstract

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.