  It is now established that the faint radio population is a mixture of
star-forming galaxies and faint active galactic nuclei (AGNs), with the former
dominating below S(1.4GHz) \sim 100 muJy and the latter at larger flux
densities. The faint radio AGN component can itself be separated into two main
classes, mainly based on the host-galaxy properties: sources associated with
red/early-type galaxies (like radio galaxies) are the dominant class down to
\sim 100 muJy; quasar/Seyfert--like sources contribute an additional 10-20\%.
One of the major open questions regarding faint radio AGNs is the physical
process responsible for their radio emission. This work aims at investigating
this issue, with particular respect to the AGN component associated with
red/early-type galaxies. Such AGNs show, on average, flatter radio spectra than
radio galaxies and are mostly compact (<= 30 kpc in size). Various scenarios
have been proposed to explain their radio emission. For instance they could be
core/core-jet dominated radio galaxies, low-power BL LACs, or
advection-dominated accretion flow (ADAF) systems. We used the Australia
Telescope Compact Array (ATCA) to extend a previous follow-up multi-frequency
campaign to 38 and 94 GHz. (abridged)
