  We introduce generalized Campanato spaces $\mathcal{L}_{p,\phi}$ on a
probability space $(\Omega,\mathcal{F},P)$, where $p\in[1,\infty)$ and
$\phi:(0,1]\to(0,\infty)$. If $p=1$ and $\phi\equiv1$, then
$\mathcal{L}_{p,\phi}=\mathrm{BMO}$. We give a characterization of the set of
all pointwise multipliers on $\mathcal{L}_{p,\phi}$.
