Let $f$ be a smooth function on the Tian-Yau space satisfying the integral normalization $\int f\omega_{TY}^{n-1}=0$ and the fast decay

$$|\nabla_{TY}^{k}f|=O(e^{-cr_{D_{1}}^{\frac{n-1}{n}}}),\quad\forall k\geq 0,$$

then there is a smooth function $u$ with $\Delta_{TY}U=f$ with fast decay

$$|\nabla_{TY}^{k}U|=O(e^{-cr_{D_{1}}^{\frac{n-1}{n}}}),\quad\forall k\geq 0,$$

where the decay rate $c>0$ may be shrinked.