Abstract
Let be the Fock–Bargmann–Hartogs domain, where . For any fixed positive integer m, we prove that there exists a unique positive integer such that is not a Lu Qi-Keng domain if and only if , which verifies a conjecture posed by Yamamori. Meanwhile, we show that the Bergman projection is bounded on if and only if p = 2. We also obtain the optimal rate of growth for holomorphic functions in .
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