Almost everywhere convergence of Bochner-Riesz means on some Sobolev   type spaces
  In this paper, we investigate the convergence of the Bochner-Riesz means on some Sobolev type spaces including $L^p$-Sobolev spaces $(p\geq 1)$ and $H^q$-Sobolev spaces $(0<q<1)$. The relation between the smoothness imposed on functions and the rate of almost everywhere convergence of the generalized Bochner-Riesz means is given. 
Dashan Fan and Fayou Zhao
math.FA