The mathematician S.Bergman defines the Bergman kernel function which plays an important role in complex variables in 1922. As we know, the bounded domain in complex space exists a unique Bergman kernel function and the explicit formulas of the Bergman kernel does matter in solving some important conjecture, such as Q.K. Lu conjecture. So it is an important research field to obtain the explicit formula of Bergman kernel function of the bounded domain. In 1950', L. K Hua worked out Bergman kernel functions with explicit formulas for four types of irreducible symmetric classical domains by using the holomorphic transitive automorphism groups, which is called Hua Method. For non-symmetric homogeneous domains, Hua Method can work out the explicit formulas of Bergman kernel functions also. In the middle of 1960's, Jiaqing Zhong and Weiping Yin constructed some new types of non-symmetric homogeneous domains and their extension spaces, and Yin work out their Bergman kernel functions by Hua Method. Besides the homogeneous domains, the Egg-domain can be obtained the Bergman kernel function in explicit formula in some cases. In general, the Egg- domain has the following form: |z_1|~(2/p1) + …+ |z-n|~(2/pn) ≤ 1 ,as the complete orthonormal system of the Egg-domain is made up of monomials, the explicit formulas of the Bergman kernel functions are calculated by summing an infinite series in some cases. By now, we are able to calculate the explicit formulas of the Bergman kernel functions on the upper two types of domains. In general, it is difficult to construct the domain whose Bergman kernel function can be obtained explicitly. So some mathematicians think the domain with explicit Bergman kernel function is worthwhile researching. Weiping Yin constructs a new type of domain with explicit Bergman kernel function, and the domain is called Hua Domain.
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