Bounds on the maximal Bochner-Riesz means for elliptic operators

Chen, Peng; Lee, Sanghyuk; Sikora, Adam; Yan, Lixin

doi:10.1090/tran/8024

Bounds on the maximal Bochner-Riesz means for elliptic operators
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Trans. Amer. Math. Soc. 373 (2020), 3793-3828 Request permission

Abstract:

We investigate $L^p$ boundedness of the maximal Bochner-Riesz means for self-adjoint operators of elliptic-type. Assuming the finite speed of propagation for the associated wave operator, from the restriction-type estimates we establish the sharp $L^p$ boundedness of the maximal Bochner-Riesz means for the elliptic operators. As applications, we obtain the sharp $L^p$ maximal bounds for the Schrödinger operators on asymptotically conic manifolds, elliptic operators on compact manifolds, or the Hermite operator and its perturbations on $\mathbb {R}^n$.

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