主 题: Commutators of the Kato square root, fractional differentiation operators for second order elliptic operators on ${ Bbb R}^n$ and related estimates
报告人: 陈艳萍 (北京科技大学)
时 间: 2014-05-13 15:00-16:00
地 点: 理科一号楼1418（主持人：刘和平）
Let $L=-{\rm div}(A\nabla)$ be a second order divergence form elliptic operator, and $A$ ia an accretive, $n\times n$ matrix with bounded measurable complex coefficients in ${\Bbb R}^n.$ 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 $L^p$ bounds for the commutator of the Kato square root $\sqrt{L}$ and $Lip_1$ function, which is a generalization of the first Calder\'{o}n commutator. In addition, we obtain the $(L^p, L^q)$ bounds for the commutators generated by Lipschitz function and some operators such as square functions, fractional integral $L^{-\frac{\alpha}{2}},\,(0<\alpha
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.
