Lemma 4.11 . [023X]

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Lemma 4.11.

In the region $|x_{2}|+1\ll x_{1}$ , we have the improved decay

\left\lVert(dd^{c}\phi_{D_{1}}^{(2)})^{n}-K_{0}\sqrt{-1}^{n^{2}}\Omega\wedge\overline{\Omega}\right\rVert_{k,\alpha,loc}=O(x_{1}^{-\frac{2n}{n-1}}x_{2}^{\frac{1}{n-1}}).