Estimates the Bergman kernel for classical domains ´E. Cartan’s

The aim of this work is to find optimal estimates for the Bergman kernels for the classical domains ℜ𝐼 (𝑚, 𝑘) ,ℜ𝐼𝐼 (𝑚) ,ℜ𝐼𝐼𝐼 (𝑚) and ℜ𝐼𝑉 (𝑛) through the Bergman kernels of balls in the spaces C𝑚𝑘,C𝑚(𝑚+1) 2 ,C𝑚(𝑚−1) 2 and C𝑛, respectively. For this, we use the statements of the Summer-Mehring theorem on the extension of the Bergman kernel and some properties of the Bergman kernel.

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