A Marcinkiewicz criterion for Lp-multipliers related to Schrödinger 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 Schrödinger operator with a constant magnetic field. We prove that if m and m ′ are locally absolutely continuous on (0, ∞ ) and then the multiplier defined by m ( t ) is bounde...

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Bibliographic Details
Published in:Science China. Mathematics 2015, Vol.58 (2), p.389-404
Main Authors: Deng, LiuRui, Ma, BoLin, Liu, ShaoYue
Format: Article
Language:English
Subjects:
Applications of Mathematics
Mathematics
Mathematics and Statistics
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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 Schrödinger operator with a constant magnetic field. We prove that if m and m ′ are locally absolutely continuous on (0, ∞ ) and then the multiplier defined by m ( t ) is bounded on L p for 2 n /( n +3) < p < 2 n /( n −3) with n ⩾ 3. Our approach is based on the estimates for the generalized Littlewood-Paley functions of the spectral representation of the Schrödinger operator with a constant magnetic field.
ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-014-4866-3