Lemma 3.7 . [015N]

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Lemma 3.7.

For $h\in C^{0}_{c}({\mathcal{U}})$ and $t\in{\mathbb{D}}^{*}$ close to 0, we have

\int_{U_{t}}h|\Omega_{t}|^{2}=(2\pi)^{p}\lambda(t)^{-p}\int_{\sigma\times(Y\cap{\mathcal{U}})}b_{\sigma}^{-1}\lambda_{\sigma}(dw)\otimes|dy|^{2}\int_{\operatorname{Log}_{t}^{-1}(w,y)}h\,\rho_{t,w,y},

(3.2)

where $dy:=dz_{p+1}\wedge\dots\wedge dz_{n}$ .