  We extend the multifractal analysis of the statistics of critical wave
functions in quantum Hall systems by calculating numerically the correlations
of local amplitudes corresponding to eigenstates at two different energies. Our
results confirm multifractal scaling relations which are different from those
occurring in conventional critical phenomena. The critical exponent
corresponding to the typical amplitude, $\alpha_0\approx 2.28$, gives an almost
complete characterization of the critical behavior of eigenstates, including
correlations. Our results support the interpretation of the local density of
states being an order parameter of the Anderson transition.
