Bounded functions in Mobius invariant Dirichlet spaces

For p is an element of (0, 1), let Q(p)(Q(p, 0)) be the space of analytic functions f on the unit disk Delta with sup(w is an element of Delta)\\f degrees phi(w)\\D-p < infinity (lim (\w\ --> 1)\\f degrees phi(w)\\D-p = 0), where \\.\\(Dp) means the weighted Dirichlet norm and phi(w) is the Mobius map of Delta onto itself wit phi(w)(0) = w. In this paper, we prove the Corona theorem for the algebra Q(p) boolean AND H-infinity (Q(p, 0) boolean AND H-infinity); then we provide a Fefferman-Stein type decomposition for Q(p)(Q(p, 0)), and finally we describe the interpolating sequences for Q(p) boolean AND H-infinity(Q(p, 0) boolean AND H-infinity). (C) 1997 Academic Press.