Almost everywhere convergence of Bochner–Riesz means for the twisted Laplacian

Abstract

Let L \mathcal L denote the twisted Laplacian in C d \mathbb {C}^d . We study almost everywhere convergence of the Bochner–Riesz mean S t δ ( L ) f S^\delta _{t}(\mathcal L) f of f ∈ L p ( C d ) f\in L^p(\mathbb C^d) as t → ∞ t\to \infty , which is an expansion of f f in the special Hermite functions. For 2 ≤ p ≤ ∞ 2\le p\le \infty , we obtain the sharp range of the summability indices δ \delta for which the convergence of S t δ ( L ) f S^\delta _{t}(\mathcal L) f holds for all f ∈ L p ( C d ) f\in L^p(\mathbb {C}^d) .