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

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.

49 pages, 2 figures

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Cited by in corpus (2)

• Almost everywhere convergence of Bochner-Riesz means for the Hermite operators
• Uniform pointwise estimates for ultraspherical polynomials