  Let $n \geq 3$ and $\Omega$ be a bounded domain in $\mathbb{C}^n$ with a
smooth negative plurisubharmonic exhaustion function $\varphi$. As a
generalization of Y. Tiba's result, we prove that any holomorphic function on a
connected open neighborhood of the support of $(i\partial \bar \partial \varphi
)^{n-2}$ in $\Omega$ can be extended to the whole domain $\Omega$. To prove it,
we combine an $L^2$ version of Serre duality and Donnelly-Fefferman type
estimates on $(n,n-1)$- and $(n,n)$- forms.
