某些华罗庚域的Bergman核函数的显式表达

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

摘要: 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.

Abstract: 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.