A Marcinkiewicz criterion for L^(p)-multipliers related to Schrodinger operators with constant magnetic fields  

作　　者：DENG Liu Rui MA Bo Lin LIU Shao Yue 

机构地区：[1]College of Economics and Management, Hunan Normal University [2]College of Mathematics and Information Engineering, Jiaxing University [3]Department of Mathematics, Xiangtan University

出　　处：《Science China Mathematics》2015年第2期389-404,共16页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.10771054 and 71201051);Natural Science Foundation of Zhejiang Province(Grant No.Y6100810);the State Scholarship Fund(Grant No.2014BQ11);Young Talents Training Plan of Hunan Normal University(GrantNo.2014YX04)

摘　　要：In this paper,we follow Dappa’s work to establish the Marcinkiewicz criterion for the spectral multipliers related to the Schrdinger operator with a constant magnetic field.We prove that if m and m′are locally absolutely continuous on(0,∞)and ‖m‖∞+sup j∈Z2j 2i+1 r|m′′(r)|dr<∞,then the multiplier defined by m(t)is bounded on Lpfor 2n/(n+3)<p<2n/(n-3)with n 3.Our approach is based on the estimates for the generalized Littlewood-Paley functions of the spectral representation of the Schrdinger operator with a constant magnetic field.In this paper,we follow Dappa’s work to establish the Marcinkiewicz criterion for the spectral multipliers related to the Schrdinger operator with a constant magnetic field.We prove that if m and m′are locally absolutely continuous on（0,∞）and ‖m‖∞＋sup j∈Z2j 2i＋1 r｜m′′（r）｜dr〈∞,then the multiplier defined by m（t）is bounded on Lpfor 2n/（n＋3）〈p〈2n/（n-3）with n 3.Our approach is based on the estimates for the generalized Littlewood-Paley functions of the spectral representation of the Schrdinger operator with a constant magnetic field.

关 键 词：magnetic Schrodinger operator spectral multiplier Riesz means 

分 类 号：O413[理学—理论物理]