【摘 要】
：
Let L =-div(A▽)be a second order divergence form elliptic operator,and A ia an accretive,n × n matrix with bounded measurable complex coefficients in Rn.First
【机 构】
：
UniversityofScienceandTechnologyBeijing
【出 处】
：
Harmonic Analysis and Applications(2014调和分析及其应用学术会议)
论文部分内容阅读
Let L =-div(A▽)be a second order divergence form elliptic operator,and A ia an accretive,n × n matrix with bounded measurable complex coefficients in Rn.First,we obtain the off-diagonal estimates for the commutators of the heat semigroup,the gradient of thesemigroup and some function spaces such as Lipschitz space and BMO space.Furthermore,we obtain the Lp bounds for the commutator of the Kato square root √L and Lip1 function,which is a generalization of the first Calderón commutator.In addition,we obtain the(Lp,Lq)bounds for the commutators generated by Lipschitz function and some operators such as square functions,fractional integral L-1/2,(0 ＜ α ＜ n)and the Riesz transform ▽L-1/2.Finally,we establish the Lp theory for the commutators generated by Sobolev space Iα(BMO)and some operators such as fractional differentiation operator Lα/2,(0 ＜ α ＜ 1),square functions related to fractional differentiation.In this work,we develop a theory for commutators associated to elliptic operators in divergence form:the heat semigroup,the gradient of the semigroup,Kato square root,fractional differentiation,fractional integral,square functions,and Riesz transforms.
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