Acta mathematica scientia,Series A ›› 2016, Vol. 36 ›› Issue (5): 832-847.

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Lp Boundedness for Some Commutators Related to Schrödinger Operator

Chen Dongxiang, Chen Xuemei   

  1. Department of Mathematics, Jiangxi Normal University, Nanchang 330022
  • Received:2015-12-13 Revised:2016-06-07 Online:2016-10-26 Published:2016-10-26
  • Supported by:

    Supported by the NSFC (11261023, 11401269, 11461033) and the Natural Science Foundation of Jiangxi Province (2014BAB201003)

Abstract:

Let H2=(-△)2+V2 be the Schrödinger type operator, where V satisfies reverse Hölder inequality. In this paper, we establish the Lp boundedness for V2H2-1, V(3)/(2)H2-1, ▽2H2-1V, ▽H2-1V(3)/(2) and that of their commutators. We also prove that ▽2H2-1V, ▽H2-1V(3)/(2) are bounded on BMOL.

Key words: BMO(Rn), Commutator, Schrö, dinger operator, Reverse Hö, lder class

CLC Number: 

  • O174.2
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