Let $(\mathcal{C},g_{\mathcal{C}})$ be the Calabi space, there is some constant $\underline{\delta}>0$ which depends only on $\mathcal{C}$ such that the following property holds: given any

(4.150)

$$\eta_{0}\in(-\underline{\delta},\underline{\delta})\setminus\{0\},$$

if $v\in C^{3K_{0},\alpha}(\mathcal{C})$ for $K_{0}\geq 3$ and $v(z,\bm{y})=O(e^{\eta_{0}z})$, then the equation

(4.151)

$$\Delta_{g_{0}}u=v$$

has a solution $u\in C^{3K_{0}+2,\alpha}(\mathcal{C})$ with

(4.152)

$$u(z,\bm{y})=O(e^{\eta z})$$

for any $\eta>\eta_{0}$.