报告人简介：

王晓峰，广州大学数学与信息科学学院教授、博士生导师。长期从事基础数学研究工作，主要研究方向为算子理论与算子代数，曾到美国进行一年的学术访问，研究成果发表于Adv. Math., Trans. AMS，Math. Z.，J. Geom. Anal., J. Oper. Theo., 中国科学等杂志，先后主持国家自然科学基金4项，获得过霍英东青年教师奖、广州市优秀教师等荣誉。

报告简介：

We introduce a class of plurisubharmonic weights on $C^n$ and develop a theory of the associated weighted Fock spaces $F^P_\phi$. The curvature assumptions are imposed on a $C^2$-regularization at bounded distance from the original weight. Thus the original weight need not be smooth or strictly plurisubharmonic, and, even when it is of class $C^2$, its complex Hessian eigenvalues need not be uniformly comparable. This provides a counterpart of Christ's doubling theory in several complex variables. We establish a global upper estimate with decay away from the diagonal and a uniform lower estimate near the diagonal for the weighted Bergman kernel. These estimates yield $L^P$ bounds for the kernel functions, boundedness of the Bergman projection, and duality and complex interpolation for the associated Fock spaces. For a certain class of weights beyond the uniformly controlled curvature setting, we construct an integral solution operator for the $ \overline{\partial}$ equation and establish scale-adapted weighted $L^P$ estimates. As an application, for all p and q, we characterize the boundedness and compactness of Hankel operators from $F^P_\phi$ to $L^q_\phi$ with possibly unbounded symbols in terms of weighted IDA spaces.