THE RATE OF ALMOST-EVERYWHERE CONVERGENCE OF BOCHNER-RIESZ MEANS ON SOBOLEV SPACES

作     者：Zhao, Junyan Fan, Dashan 

作者机构：Zhejiang Univ Dept Math Hangzhou 310027 Zhejiang Peoples R China Univ Wisconsin Dept Math Sci Milwaukee WI 53201 USA 

出 版 物：《ANNALS OF FUNCTIONAL ANALYSIS》 (Ann. Funct. Anal.)

年 卷 期：2019年第10卷第1期

页      面：29-45页

核心收录：

基　　金：National Natural Science Foundation of China (NSFC) [11771388, 11371316] NSFC [11471288, 11601456] 

主　　题：Bochner-Riesz means Sobolev spaces almost-everywhere convergence saturation of approximation maximal functions Fourier series 

摘      要：We investigate the convergence rate of the generalized Bochner-Riesz means S-R(delta,gamma) on L-P-Sobolev spaces in the sharp range of delta and p (p = 2). We give the relation between the smoothness imposed on functions and the rate of almost-everywhere convergence of S-R(delta,gamma). As an application, the corresponding results can be extended to the n-torus T-n by using some transference theorems. Also, we consider the following two generalized Bochner-Riesz multipliers, (1 - vertical bar xi vertical bar(gamma 1))(+)(delta) and (1 - vertical bar xi vertical bar(gamma 2))(-)(delta), where gamma(1), gamma(2), delta are positive real numbers. We prove that, as the maximal operators of the multiplier operators with respect to the two functions, their L-2(vertical bar x vertical bar(-beta))-boundedness is equivalent for any gamma(1), gamma(2) and fixed delta.