  The field strength superfield of IIB supergravity on $AdS_5\xz S^5$ is
expanded in harmonics on $S^5$ with coefficients which are $D=5, N=8$ chiral
superfields. On the boundary of $AdS_5$ these superfields map to $D=4,N=4$
chiral superfields and both sets of superfields obey additional fourth-order
constraints. The constraints on the $D=4,N=4$ chiral fields are solved using
harmonic superspace in terms of prepotential superfields which couple in a
natural way to composite operator multiplets of the boundary $N=4,D=4$
superconformal field theory.
