BOUNDARY MULTIPLIERS OF A FAMILY OF MOBIUS INVARIANT FUNCTION SPACES

For 1 < p < infinity and 0 < s < 1, we consider the function spaces Q(s)(p)(T) that appear naturally as the space of boundary values of a certain family of analytic Mobius invariant function spaces on the the unit disk. In this paper, we give a complete description of the pointwise multipliers going from Q(s)(p1) (T) to Q(r)(p2)(T) for all ranges of 1 < p(1),p(2) < infinity and 0 < s,r < 1. The spectra of such multiplication operators is also obtained.