Bounds on the maximal Bochner-Riesz means for elliptic operators

I will discuss $L^p$ boundedness of the maximal Bochner-Riesz means for self-adjoint operators of elliptic type which satisfy the finite speed of propagation for the associated wave operator. The main point of the discussion is the relationship between the sharp $L^p$ boundedness of the maximal Bochner-Riesz means and the restriction type estimates. The talk is base on joint work with Peng Chen, Sanghyuk Lee and Lixin Yan.