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中文摘要：
研究一类带变象征的拟微分算子Tf（x）的高阶交换子的L2有界性，推广了Chanillo的结论，并得到更优的结果。当ω∈A2,T∈Lm ρ,δ,0≤δ〈ρ〉1/2。且m〈0时，若b∈BMO，假设结论对t-1阶成立，根据拟微分算子的线性性质，运用Stein．Weiss限制性插值定理，得到对于任意的θ∈[0，2π]，有f∈L2（ωe2bcosθ）。利用Minkowski不等式和Plancherel定理，证明结论对t阶也成立，由此得到带变象征拟微分算子的高阶交换子[b，T]mf（x）=∫Rna（x,z）f（z）e2πix·ξ（b（x）-b（z））mdz的加权L2有界性质。
英文摘要：
The boundedness of higher order commutators generated by Pseudo-differential operators Tf（x） and BMO functions is studied on weighted L2 spaces, which generalized the Chanillo＇ s conclusions in 1997, and better result was obtained. When ω∈A2,T∈Lm ρ,δ,0≤δ〈ρ〉1/2 and m〈0,let b∈BMO ,under the assumption that the conclusion has been established for t - 1 order, it is investigated f∈L2（ωe2bcosθ） for arbitrary θ∈[0,2π] according to the linear property of pseudo-differential operator and using the stein-weiss restricted interpolation theorem. Finally, using the Minkowski inequality and Plancherel theorem, it is proven that the conclusion was also correct for t order. From which, the weighted L2 boundedness for higher order commutators with variable symbol of pseudo-differential operator [b,T]mf（x）=∫Rna（x,z）f（z）e2πix·ξ（b（x）-b（z））mdz is obtained.
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