  We calculate the momentum-dependent potentials for $K^+$ and $K^-$ mesons in
a dispersion approach at nuclear density $\rho_0$ using the information from
the vacuum $K^+ N$ and $K^- N$ scattering amplitudes, however, leaving out the
resonance contributions for the in-medium analysis. Whereas the $K^+$ potential
is found to be repulsive ($\approx$ + 30 MeV) and to show only a moderate
momentum dependence, the $K^-$ selfenergy at normal nuclear matter density
turns out to be $\approx$ - 200 MeV at zero momentum in line with kaon atomic
data, however, decreases rapidly in magnitude for higher momenta. The antikaon
production in p + A reactions is calculated within a coupled transport approach
and compared to the data at KEK including different assumptions for the
antikaon potentials. Furthermore, detailed predictions are made for $p +
^{12}C$ and $p + ^{207}Pb$ reactions at 2.5 GeV in order to determine the
momentum dependent antikaon potential experimentally.
