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

作　　者：李澎涛 彭立中 

机构地区：[1]Department of Mathematics,Shantou University [2]LMAM School of Mathematical Sciences,Peking University

出　　处：《Acta Mathematica Scientia》2012年第2期568-578,共11页数学物理学报（B辑英文版）

基　　金：supported by NSFC 11171203, S2011040004131;STU Scientific Research Foundation for Talents TNF 10026;supported by NSFC No.10990012,10926179;RFDP of China No.200800010009

摘　　要：Let L = -△Hn ＋ V be a SchrSdinger operator on Heisenberg group Hn, where AHn is the sublaplacian and the nonnegative potential V belongs to the reverse HSlder class BQ/2 where Q is the homogeneous dimension of Hn. Let T1 = （--△Hn ＋V）-1V, T2 = （-△Hn ＋V）-1/2V1/2, and T3 = （--AHn ＋V）-I/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.Let L = -△Hn ＋ V be a SchrSdinger operator on Heisenberg group Hn, where AHn is the sublaplacian and the nonnegative potential V belongs to the reverse HSlder class BQ/2 where Q is the homogeneous dimension of Hn. Let T1 = （--△Hn ＋V）-1V, T2 = （-△Hn ＋V）-1/2V1/2, and T3 = （--AHn ＋V）-I/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.

关 键 词：COMMUTATOR BMO Heisenberg group BOUNDEDNESS Riesz transforms as-sociated to SchrSdinger operators 

分 类 号：O175.29[理学—数学]