BOUNDS ON THE MAXIMAL BOCHNER-RIESZ MEANS FOR ELLIPTIC OPERATORS

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 Schrodinger operators on asymptotically conic manifolds, elliptic operators on compact manifolds, or the Hermite operator and its perturbations on R-n.