I'm having a brain freeze.

Let $B$ be the space of complex valued measurable functions on the unit disk in the complex plane with essential supremum less than 1. Then, the universal Teichmuller space $T$ can be though of as a quotient space of $B$.

I vaguely recall reading somewhere that for every point $p \in T$ has a unique representative of the form

$\mu(z) = k \frac{\bar{q}}{q}$, where $q$ is a holomorphic function on the unit disk.

First of all, am I crazy and am remembering something that's completely off?

Secondly, if there is a statement like that, where should I be looking?