某些华罗庚域的Bergman核函数的显式表达

通过构造超几何函数和球型积分变换方法，给出了更多变量的新域$E(k,q_{2},\cdots,q_{m}, \Omega,p_{2},\cdots,p_{m}$上的Bergman核函数的显示表达式,其中$\Omega$是指任意不可约有界圆型齐性域，$k,m,q_{2},\cdots,q_{m}$都是正整数, $p_{2},\cdots,p_{m}$都是正实数，$N(Z,Z)$是$\Omega$的一般范数.而且，当$\Omega$是4大类的不可约的对称典型域时，上述域就是华罗庚域.同时可以得出相应华罗庚域上的Bergman核函数的显示表达式.

Explicit formulas of the Bergman kernel functions for some domains of Hua Luo-Geng

The explicit formulas of the Bergman kernel functions for some new domains of Hua Luo-Geng are provided by constructing hypergeometric function and spherical integral transform method. Among them,$\Omega$ is any irreducible bounded circular homogeneity domain, $k,m,q_{2},\cdots,q_{m}$ are all positive integers, $p_{2},\cdots,p_{m}$ are all positive number, $N(Z, Z)$ is the norm of $\Omega$.And when $\Omega$ is four categories of irreducible symmetrical typical domain, then the domain is Hua Luo-Geng domain. And the explicit formulas of the Bergman kernel functions for corresponding domains of Hua Luo-Geng can be drawn.