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.

中文翻译：

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Bochner–Riesz几乎所有地方的收敛都意味着Heisenberg型群

我们证明了Bochner–Riesz方法几乎在任何地方都收敛的结果 ${\mathrm{大号}}^p$ 在海森堡型群上起作用，产生了一个 $p>\mathrm{2个}$为此，收敛适用于任意小的阶数。证明取决于减少权重${\mathrm{大号}}^{\mathrm{2个}}$ 最大Bochner–Riesz算子的估计到非最大算子的相应估计，以及“双重Sobolev跟踪引理”，其证明基于Jacobi多项式的精确估计。