A Marcinkiewicz criterion for L~p-multipliers related to Schrdinger operators with constant magnetic fields |
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作者姓名: | DENG Liu Rui MA Bo Lin LIU Shao Yue |
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作者单位: | College of Economics and Management, Hunan Normal University;College of Mathematics and Information Engineering, Jiaxing University;Department of Mathematics, Xiangtan University |
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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)p2n/(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.
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关 键 词: | criterion absolutely multiplier operators kernel locally smoothness estimates coordinates satisfy |
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