Theorems demonstrate the equivalence of pseudoconvexity and exhaustion functions in bounded domains, revealing implications.
Following the way of J. Ning, H. Zhang, and X. Zhou [23], we show some properties of the (2 β π)-Bergman kernels by applying πΏ 2βπ extension theorem. We also show that for any bounded domain in β π , it is pseudoconvex if and only if its (2β π)-Bergman kernel is an exhaustion function, for any 0 < π < 2. As an application, we give a negative answer to a conjecture of Tsuji.
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Abd-Allah et al. (2025) studied this question.
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