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Almost everywhere convergence of Bochner-Riesz means on Heisenberg-type groups (1908.04049v2)
Published 12 Aug 2019 in math.CA and math.FA
Abstract: 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.