A Marcinkiewicz criterion for L~p-multipliers related to Schrdinger operators with constant magnetic fields

In this paper,we follow Dappa’s work to establish the Marcinkiewicz criterion for the spectral multipliers related to the Schrdinger 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 de...

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Bibliographic Details
Published in中国科学：数学英文版 no. 2; pp. 389 - 404
Main Author DENG Liu Rui MA Bo Lin LIU Shao Yue
Format Journal Article
LanguageEnglish
Published 2015
Subjects
Littlewood
乘法器
恒定磁场
恒磁场
标准
绝对连续
薛定谔
运营商
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Summary:In this paper,we follow Dappa’s work to establish the Marcinkiewicz criterion for the spectral multipliers related to the Schrdinger 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 Schrdinger operator with a constant magnetic field.
Bibliography:magnetic Schrdinger operator;spectral multiplier;Riesz means
In this paper,we follow Dappa’s work to establish the Marcinkiewicz criterion for the spectral multipliers related to the Schrdinger 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 Schrdinger operator with a constant magnetic field.
11-1787/N
ISSN:1674-7283
1869-1862