Lp BOUNDEDNESS OF COMMUTATOR OPERATOR ASSOCIATED WITH SCHRÖDINGER OPERATORS ON HEISENBERG GROUP

doi:10.1016/S0252-9602(12)60039-3

数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (2): 568-578.doi: 10.1016/S0252-9602(12)60039-3

L^p BOUNDEDNESS OF COMMUTATOR OPERATOR ASSOCIATED WITH SCHRÖDINGER OPERATORS ON HEISENBERG GROUP

李澎涛|彭立中

Department of Mathematics, Shantou University, Shantou 515063, China； LMAM School of Mathematical Sciences, Peking University, Beijing 100871, China

收稿日期:2009-09-30 修回日期:2010-07-15 出版日期:2012-03-20 发布日期:2012-03-20
基金资助:
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.

L^p BOUNDEDNESS OF COMMUTATOR OPERATOR ASSOCIATED WITH SCHRÖDINGER OPERATORS ON HEISENBERG GROUP

LI Peng-Tao, PENG Li-Zhong

Department of Mathematics, Shantou University, Shantou 515063, China； LMAM School of Mathematical Sciences, Peking University, Beijing 100871, China

Received:2009-09-30 Revised:2010-07-15 Online:2012-03-20 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.

摘要/Abstract

摘要：

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 B_Q_/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, T_i], i = 1, 2, 3 are bounded on some L^p(Hⁿ), where b ∈ BMO(Hⁿ). Note that the kernel of T_i, i = 1, 2, 3 has no smoothness.

关键词: Commutator, BMO, Heisenberg group, boundedness, Riesz transforms as-sociated to Schr¨odinger operators

Abstract:

Key words: Commutator, BMO, Heisenberg group, boundedness, Riesz transforms as-sociated to Schr¨odinger operators

中图分类号:

47B32

李澎涛, 彭立中. L^p BOUNDEDNESS OF COMMUTATOR OPERATOR ASSOCIATED WITH SCHRÖDINGER OPERATORS ON HEISENBERG GROUP[J]. 数学物理学报(英文版), 2012, 32(2): 568-578.

LI Peng-Tao, PENG Li-Zhong. L^p BOUNDEDNESS OF COMMUTATOR OPERATOR ASSOCIATED WITH SCHRÖDINGER OPERATORS ON HEISENBERG GROUP[J]. Acta mathematica scientia,Series B, 2012, 32(2): 568-578.

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L^p BOUNDEDNESS OF COMMUTATOR OPERATOR ASSOCIATED WITH SCHRÖDINGER OPERATORS ON HEISENBERG GROUP

L^p BOUNDEDNESS OF COMMUTATOR OPERATOR ASSOCIATED WITH SCHRÖDINGER OPERATORS ON HEISENBERG GROUP

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