Acta mathematica scientia, Series B >
Lp BOUNDEDNESS OF COMMUTATOR OPERATOR ASSOCIATED WITH SCHRÖDINGER OPERATORS ON HEISENBERG GROUP
Received date: 2009-09-30
Revised date: 2010-07-15
Online published: 2012-03-20
Supported by
The first author was supported by NSFC 11171203, S2011040004131, and STU Scientific Research Foundation for Talents TNF 10026. The second author was supported by NSFC No. 10990012, 10926179, and RFDP of China No.200800010009.
Let L = −△Hn+V be a Schr¨odinger operator on Heisenberg group Hn, where △Hn is the sublaplacian and the nonnegative potential V belongs to the reverse H¨older class BQ/2, where Q is the homogeneous dimension of Hn. Let T1 = (−△Hn+V )−1V , T2 =(−△Hn+V )−1/2V 1/2, and T3 = (−△Hn+V )−1/2∇Hn, then we verify that [b, Ti], i = 1, 2, 3 are bounded on some Lp(Hn), where b ∈ BMO(Hn). Note that the kernel of Ti, i = 1, 2, 3 has no smoothness.
LI Peng-Tao , PENG Li-Zhong . Lp BOUNDEDNESS OF COMMUTATOR OPERATOR ASSOCIATED WITH SCHRÖDINGER OPERATORS ON HEISENBERG GROUP[J]. Acta mathematica scientia, Series B, 2012 , 32(2) : 568 -578 . DOI: 10.1016/S0252-9602(12)60039-3
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