$$L^2$$ Extension of $${{\bar{\partial }}}$$-Closed Forms on Weakly Pseudoconvex Kähler Manifolds

Combining V. Koziarz’s observation about the regularity of some modified section related to initial extension with J. McNeal–D. Varolin’s argument, we generalize two theorems McNeal–Varolin for \(L^2\) of\({{\bar{\partial }}}\)-closed high-degree forms on a Stein manifold weakly pseudoconvex Kähler case under mixed positivity conditions.