We investigate the convergence rate of the generalized Bochner–Riesz means on -Sobolev spaces in the sharp range of and (). We give the relation between the smoothness imposed on functions and the rate of almost-everywhere convergence of . As an application, the corresponding results can be extended to the -torus by using some transference theorems. Also, we consider the following two generalized Bochner–Riesz multipliers, and , where , , are positive real numbers. We prove that, as the maximal operators of the multiplier operators with respect to the two functions, their -boundedness is equivalent for any , and fixed .
"The rate of almost-everywhere convergence of Bochner–Riesz means on Sobolev spaces." Ann. Funct. Anal. 10 (1) 29 - 45, February 2019. https://doi.org/10.1215/20088752-2018-0006