An application of Chen's theorem to convergence of Fourier multiplier transforms  

作　　者：SHI Xian-liang CHEN Yang HU Lan 

机构地区：[1]College of Mathematics and Computer Science, Key Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP) (Ministry of Education of China), Hunan Normal University

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2013年第4期455-464,共10页高校应用数学学报（英文版）（B辑）

基　　金：Supported by the National Natural Science Foundation of China(11071065,11171306)

摘　　要：Let V be a star shaped region. In 2006, Colzani, Meaney and Prestini proved that if function f satisfies some condition, then the multiplier transform with the characteristic function of tV as the multiplier tends to f almost everywhere, when t goes to∞. In this paper we use a Theorem established by K.K.Chen to show that if we change their multiplier, then the condition on f can be weakened.Let V be a star shaped region. In 2006, Colzani, Meaney and Prestini proved that if function f satisfies some condition, then the multiplier transform with the characteristic function of tV as the multiplier tends to f almost everywhere, when t goes to∞. In this paper we use a Theorem established by K.K.Chen to show that if we change their multiplier, then the condition on f can be weakened.

关 键 词：Fourier transform MULTIPLIER SUMMABILITY CONVERGENCE almost everywhere 

分 类 号：O174.22[理学—数学]