Almost everywhere convergence of Bochner-Riesz means for the twisted Laplacian. (English) Zbl 07905996
Summary: Let \(\mathcal{L}\) denote the twisted Laplacian in \(\mathbb{C}^d\). We study almost everywhere convergence of the Bochner-Riesz mean \(S^\delta_t(\mathcal{L}) f\) of \(f\in L^p(\mathbb{C}^d)\) as \(t\to \infty \), which is an expansion of \(f\) in the special Hermite functions. For \(2\le p\le \infty \), we obtain the sharp range of the summability indices \(\delta\) for which the convergence of \(S^\delta_t(\mathcal{L}) f\) holds for all \(f\in L^p(\mathbb{C}^d)\).
MSC:
| 42A20 | Convergence and absolute convergence of Fourier and trigonometric series |
| 42B15 | Multipliers for harmonic analysis in several variables |
| 42B25 | Maximal functions, Littlewood-Paley theory |
| 42C10 | Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) |
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