  We characterize the restrictions of B\'ekoll\'e--Bonami weights of bounded
hyperbolic oscillation, to subsets of the unit disc, thus proving an analogue
of Wolff's restriction theorem for Muckenhoupt weights. Sundberg proved a
discrete version of Wolff's original theorem, by characterizing the trace of
$BMO$-functions onto interpolating sequences. We consider an analogous question
in our setting, by studying the trace of Bloch functions. Through Makarov's
probabilistic approach to the Bloch space, our question can be recast as a
restriction problem for dyadic martingales with uniformly bounded increments.
