Logarithmic Akizuki--Nakano vanishing theorems on weakly pseudoconvex K\"{a}hler manifolds

In this paper, we establish a logarithmic vanishing theorem on weakly pseudoconvex K"ahler manifolds, where the divisor may have infinitely many irreducible components. This result serves as a generalization of Norimatsu’s findings on compact K"ahler manifolds. We derive vanishing theorems for certain direct image sheaves as a direct corollary.