加权调和Bergman核及其诱导的度量矩阵

Weighted Harmonic Bergman Kernel on the Unit Ball

在Rn中的有界域上建立加权调和Bergman核,并得出单位球的加权调和Bergman核的表达式;利用加权调和Bergman核在Rn的有界域上构造度量矩阵;得到关于调和映射的Jacobi矩阵与度量矩阵之间的一个不等式.

We construct weighted harmonic Bergman kernel on the bounded domain of Rm, and obtain weighted harmonic Bergman kernel on the unit Ball. We have constructed the positive definite metric matrixes for the bounded domains of Rn and proved an inequality which is about the Jacobi matrix of a harmonic mapping on a bounded domain of Rn and the metric matrix of the same bounded domain.