  Context: Submillimeter galaxies are a population of dusty star-forming
galaxies at high redshift. Measuring their properties will help relate them to
other types of galaxies, both at high and low redshift. This is needed in order
to understand the formation and evolution of galaxies. Aims: We use
gravitational lensing by galaxy clusters to probe the faint and abundant
submillimeter galaxy population down to a lower flux density level than what
can be achieved in blank-field observations. Methods: We use the LABOCA
bolometer camera on the APEX telescope to observe five cluster of galaxies at a
wavelength of 870 micron. The final maps have an angular resolution of 27.5
arcsec and a point source noise level of 1.2-2.2 mJy. We model the mass
distribution in the clusters as superpositions of spherical NFW halos and
derive magnification maps that we use to calculate intrinsic flux densities as
well as area-weighted number counts. We also use the positions of Spitzer MIPS
24 micron sources in four of the fields for a stacking analysis. Results: We
detected 37 submm sources, out of which 14 have not been previously reported.
One source has a sub-mJy intrinsic flux density. The derived number counts are
consistent with previous results, after correction for gravitational
magnification and completeness levels. The stacking analysis reveals an
intrinsic 870 micron signal of 390 \pm 27 microJy at 14.5 sigma significance.
We study the S_{24 micron} - S_{870 micron} relation by stacking on subsamples
of the 24 micron sources and find a linear relation at S_{24 micron} < 300
microJy, followed by a flattening at higher 24 micron flux densities. The
signal from the significantly detected sources in the maps accounts for 13% of
the Extragalactic Background Light discovered by COBE, and the stacked signal
accounts for 11%.
