  With a goal of searching for accreting intermediate-mass black holes (IMBHs),
we report the results of ultra-deep Jansky VLA radio continuum observations of
the cores of three Galactic globular clusters: M15, M19, and M22. We reach rms
noise levels of 1.5-2.1 uJy/beam at an average frequency of 6 GHz. No sources
are observed at the center of any of the clusters. For a conservative set of
assumptions about the properties of the accretion, we set 3-sigma upper limits
on IMBHs from 360-980 M_sun. These limits are among the most stringent obtained
for any globular cluster. They add to a growing body of work that suggests
either (a) IMBHs ~> 1000 M_sun are rare in globular clusters, or (b) when
present, IMBHs accrete in an extraordinarily inefficient manner.
