Abstract: In the 90's a type of Möbius invariant function spaces, called $Q_s$, were introduced, and the function theory of these spaces was fruitfully developed. Nevertheless, there are some natural problems in these spaces that remained open, for example, to give a complete characterization of the algebra of multipliers of these spaces or the corona theorem for the multipliers of $Q_s$. In this talk we are going to solve both problems.