  Model-independent constraints on hadronic form factors, in particular those
describing exclusive semileptonic decays, can be derived from the knowledge of
field correlators calculated in perturbative QCD, using analyticity and
unitarity. The location of poles corresponding to below-threshold resonances,
i.e., stable states that cannot decay into a pair of hadrons from the crossed
channel of the form factor, must be known a priori, and their effect, accounted
for through the use of Blaschke factors, is to reduce the strength of the
constraints in the semileptonic region. By contrast, above-threshold resonances
appear as poles on unphysical Riemann sheets, and their presence does not
affect the original model-independent constraints. We discuss the possibility
that the above-threshold poles can provide indirect information on the form
factors on the first Riemann sheet, either through information from their
residues or by constraining the discontinuity function. The bounds on form
factors can be improved by imposing, in an exact way, the additional
information in the extremal problem. The semileptonic $K\to \pi\ell \nu$ and
$D\to \pi\ell\nu$ decays are considered as illustrations.
