Restrictions of Békollé–Bonami weights and Bloch functions

We characterize the restrictions of Békollé–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 Bloch dyadic martingales on the unit circle.