  The deep near-infrared luminosity function of AC118, a cluster of galaxies at
z=0.3, is presented. AC118 is a bimodal cluster, as evidenced both by our
near-infrared images of lensed galaxies, by public X-ray Rosat images and by
the spatial distribution of bright galaxies. Taking advantage of the extension
and depth of our data, which sample an almost unexplored region in the depth
vs. observed area diagram, we derive the luminosity function (LF), down to the
dwarf regime (M*+5), computed in several cluster portions. The overall LF,
computed on a 2.66 Mpc2 areas (H_0=50 km/s/Mpc), has an intermediate slope
(alpha=-1.2). However, the LF parameters depend on the surveyed cluster region:
the central concentration has 2.6^{+5.1}_{-1.7} times more bright galaxies and
5.3^{+7.2}_{-2.3} times less dwarfs per typical galaxy than the outer region,
which includes galaxies at an average projected distance of ~580 kpc (errors
are quoted at the 99.9 % confidence level). The LF in the secondary AC118 clump
is intermediate between the central and outer one. In other words, the
near-infrared AC118 LF steepens going from high to low density regions. At an
average clustercentric distance of ~580 kpc, the AC118 LF is statistically
indistinguishable from the LF of field galaxies at similar redshift, thus
suggesting that the hostile cluster environment plays a minor role in shaping
the LF at large clustercentric distances, while it strongly affects the LF at
higher galaxy density.
