Boundary behavior of the Kobayashi metric near a point of infinite type

Under a potential-theoretical hypothesis named $f$-Property with $f$ satisfying ${\displaystyle {\int }_t^{\mathrm{\infty }}{\displaystyle \frac{da}{af(a)}}<\mathrm{\infty }}$, we show that the Kobayashi metric $K(z,X)$ on a weakly pseudoconvex domain $\text{Om}$, satisfies the estimate $K(z,X)\ge Cg({\delta }_{\text{Om}}(x{)}^{-1})\mathrm{\mid }X\mathrm{\mid }$ for any $X\in T^{1,0}\text{Om}$ where $(g(t){)}^{-1}$ denotes the above integral and ${\delta }_{\text{Om}}(z)$ is the distance from $z$ to $b\text{Om}$.