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∈Lmρ,δ,0≤δ<ρ<12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。
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.
出处
《黑龙江大学自然科学学报》
CAS
北大核心
2013年第3期341-343,共3页
Journal of Natural Science of Heilongjiang University
基金
国家自然科学基金资助项目(11161042
11071250)
关键词
拟微分算子
高阶交换子
L2有界性
BMO函数
pseudo-differential operator
higher order commutators
L2 boundedness
BMO function
