A Step on (2 − 𝜖)-Bergman Kernel for Bounded Domains in ℂ �

Following the way of J. Ning, H. Zhang, and X. Zhou [23], we show some properties of the (2 − 𝜖)-Bergman kernels by applying 𝐿 2−𝜖 extension theorem. We also show that for any bounded domain in ℂ 𝑛 , it is pseudoconvex if and only if its (2− 𝜖)-Bergman kernel is an exhaustion function, for any 0 < 𝜖 < 2. As an application, we give a negative answer to a conjecture of Tsuji.