  Given a suitably regular nonnegative function $\omega$ on $(0,1]$, let
$\mathcal B_\omega$ denote the space of all holomorphic functions $f$ on the
unit ball $\mathbb B_n$ of $\mathbb C^n$ that satisfy $$|\nabla f(z)|\le
C\frac{\omega(1-|z|)}{1-|z|},\qquad z\in\mathbb B_n,$$ with some fixed
$C=C_f>0$. We obtain a new characterization of $\mathcal B_\omega$ functions in
terms of their moduli.
