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Bochner-Riesz mean for the twisted Laplacian in $\mathbb R^2$ (2310.12604v1)
Published 19 Oct 2023 in math.CA
Abstract: We study the Bochner-Riesz problem for the twisted Laplacian $\mathcal L$ on $\mathbb R2$. For $p\in [1, \infty]\setminus{2}$, it has been conjectured that the Bochner-Riesz means $S_\lambda\delta(\mathcal L) f$ of order $\delta$ converges in $Lp$ for every $f\in Lp$ if and only if $\delta> \max(0,|(p-2)/p|-1/2)$. We prove the conjecture by obtaining uniform $Lp$ bounds on $S_\lambda\delta(\mathcal L)$ up to the sharp summability indices.