Pointwise lower bounds in growth spaces with little o conditions

Pointwise lower bounds on the open unit disc $\text{bbD}$ for the sum of the moduli of two analytic functions $f$ and $g$ (or their derivatives) are known in several cases, like $f,g$ belonging to the Bloch space $\text{cB}$, $BMOA$ or the weighted Hardy space $H_{\omega }^{\mathrm{\infty }}$. We find complementary results of Ramey-Ullrich and Abakumov-Doubtsov for functions with little o conditions.