Interpolating by functions from model subspaces in $H^1$

Given an interpolating Blaschke product $B$ with zeros $\{a_j\}$, we seek to characterize the sequences of values $\{w_j\}$ for which the interpolation problem $$f(a_j)=w_j(j=1,2,\dots )$$ can be solved with a function $f$ from the model subspace $H^1\cap B\overline{H_0^1}$ of the Hardy space $H^1$.