L boundedness of commutator operator associated with schrödinger operators on heisenberg group |
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Authors: | Li Pengtao Peng Lizhong |
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Institution: | 1. Department of Mathematics, Shantou University, Shantou 515063, China;2. LMAM School of Mathematical Sciences, Peking University, Beijing 100871, China |
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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/V21/2, and
T3=(−ΔHn+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. |
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Keywords: | Commutator BMO Heisenberg group boundedness Riesz transforms associated to Schrö dinger operators |
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