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L boundedness of commutator operator associated with schrödinger operators on heisenberg group
Authors:Li Pengtao  Peng Lizhong
Institution:1. Department of Mathematics, Shantou University, Shantou 515063, China;2. LMAM School of Mathematical Sciences, Peking University, Beijing 100871, China
Abstract:Let L = −ΔHn + V be a Schrödinger operator on Heisenberg group Hn, where ΔHn is the sublaplacian and the nonnegative potential V belongs to the reverse Hölder class BQ/2, where Q is the homogeneous dimension of Hn  . Let T1=(−ΔHn+V)−1V,T2=(−ΔHn+V)−1/V21/2T1=(ΔHn+V)1V,T2=(ΔHn+V)1/2V1/2, and T3=(−ΔHn+V)−1/2HnT3=(ΔHn+V)1/2Hn, 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.
Keywords:Commutator  BMO  Heisenberg group  boundedness  Riesz transforms associated to Schrö  dinger operators
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