ScalingStacks

Lemma 3.26 . [043P]

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Lemma 3.26.

Over the disc {|μ→|a≤13A1/2}\{|\vec{\mu}|_{a}\leq\frac{1}{3}A^{1/2}\}

|β~i−Ψ1−1∗βi|≤CA−1/2|μ→|a,|∇gak(β~i−Ψ1−1∗βi)|ga≤CA−k/2.|\tilde{\beta}_{i}-\Psi_{1}^{-1*}\beta_{i}|\leq CA^{-1/2}|\vec{\mu}|_{a},\quad|\nabla^{k}_{g_{a}}(\tilde{\beta}_{i}-\Psi_{1}^{-1*}\beta_{i})|_{g_{a}}\leq CA^{-k/2}.

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