  We establish the framework for the comparison of $\pi K$ scattering
amplitudes from SU(3) chiral perturbation theory with suitable dispersive
representations which result from the combination of certain fixed-t dispersion
relations with dispersion relations on hyperbolic curves. This allows for
predictions for some combinations of low energy constants appearing in higher
order calculations of chiral perturbation theory. Using a simple
parametrization for the lowest partial waves, first estimates for some
combinations are presented.
