Pointwise lower bounds in growth spaces with little o conditions

Abstract

Pointwise lower bounds on the open unit disc $\bbD$ 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 $\cB$, $BMOA$ or the weighted Hardy space $H_{\omega }^{\infty }$. We find complementary results of Ramey-Ullrich and Abakumov-Doubtsov for functions with little o conditions.

To appear in Math. Scandinavica