Equation 6.4.5038AC5695B6F

\begin{equation} \int \sum _{j,k}\varphi _{j\bar k}f_ j\bar f_ k\mathrm e^{-\varphi }\, \mathrm dV \le (1+t^{-1})\| T^*f\| _{\mathcal H_0}^2+\| Sf\| _{\mathcal H_2}^2 +(1+t)\int |f|^2|\bar\partial \psi |^2\mathrm e^{-\varphi }\, \mathrm dV. \end{equation}