In this talk, I will discuss the convergence of the Bochner-Riesz means on the block-Sobolev spaces. The relation between the smoothness imposed on blocks and the rate of almost everywhere convergence of the generalized Bochner-Riesz means at the critical index is given. The main theorem solves an open question in [S. Lu and S. Wang, Spaces generated by smooth blocks,  Constr. Approx., 8 (1992), no. 3, 331--341].

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