  Kinetic regime of capillary wave turbulence is classically regarded in terms
of three-wave interactions with the exponent of power energy spectrum being
$\nu=-7/4$ (two-dimensional case). We show that a number of assumptions
necessary for this regime to occur can not be fulfilled. Four-wave interactions
of capillary waves should be taken into account instead, which leads to
exponents $\nu=-13/6$ and $\nu=-3/2$ for one- and two-dimensional wavevectors
correspondingly. It follows that for general dispersion functions of decay
type, three-wave kinetic regime need not prevail and higher order resonances
may play a major role.
  Accepted for publication.
