  We have used the Arecibo L-band Feed Array to map three regions, each of 5
square degrees, around the isolated galaxies NGC 1156, UGC 2082, and NGC 5523.
In the vicinity of these galaxies we have detected two dwarf companions: one
near UGC 2082, previously discovered by ALFALFA, and one near NGC 1156,
discovered by this project and reported in an earlier paper. This is
significantly fewer than the 15.4 $^{+1.7}_{-1.5}$ that would be expected from
the field HI mass function from ALFALFA or the 8.9 $\pm$ 1.2 expected if the HI
mass function from the Local Group applied in these regions. The number of
dwarf companions detected is, however, consistent with a flat or declining HI
mass function as seen by a previous, shallower, HI search for companions to
isolated galaxies.We attribute this difference in Hi mass functions to the
different environments in which they are measured. This agrees with the general
observation that lower ratios of dwarf to giant galaxies are found in lower
density environments.
