Bounds on the maximal Bochner-Riesz means for elliptic operators

Abstract

We investigate L p 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 L^p boundedness of the maximal Bochner-Riesz means for the elliptic operators. As applications, we obtain the sharp L p 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 R n \mathbb {R}^n .