Lemma 2.21 . [040X]

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Lemma 2.21.

In the situation of Lemma 2.20, if $C_{3}$ is sufficiently large, then

\left\lVert\Delta_{g^{(2)}}(\chi_{1}G_{\text{Taub}}f)-f\right\rVert_{C^{k,\alpha}_{\delta,\tau}(\mathbb{C}^{3}\cap\{|\vec{\mu}|_{a}>2C_{3}\})}\leq CC_{3}^{-\epsilon}\ll 1.