  We present the results of a pilot JVLA project aimed at studying the bulk of
the radio-emitting AGN population, unveiled by the NVSS/FIRST and SDSS
surveys.We obtained A-array observations at the JVLA at 1.4, 4.5, and 7.5 GHz
for 12 sources of the SDSS/NVSS sample. The radio maps reveal compact
unresolved or slightly resolved radio structures on a scale of 1-3 kpc, with
only one exception of a FRI/FRII source extended over $\sim$40 kpc. We isolate
the radio core component in most of them. The sample splits into two groups.
Four sources have small black hole (BH) masses (mostly $\sim$10$^{7}$
M$_{\odot}$) and are hosted by blue galaxies, often showing evidence of a
contamination from star formation to their radio emission and associated with
radio-quiet AGN. The second group consists in seven radio-loud AGN, which live
in red massive ($\sim10^{11}$ M$_{\odot}$) early-type galaxies, with large BH
masses ($\gtrsim$10$^{8}$ M$_{\odot}$), and spectroscopically classified as Low
Excitation Galaxies, all characteristics typical of FRI radio galaxies. They
also lie on the correlation between radio core power and [O III] line
luminosity defined by FRIs. However, they are more core dominated (by a factor
of $\sim$30) than FRIs and show a deficit of extended radio emission. We dub
these sources 'FR0' to emphasize their lack of prominent extended radio
emission, the single distinguishing feature with respect to FRIs. The
differences in radio properties between FR0s and FRIs might be ascribed to an
evolutionary effect, with the FR0 sources undergoing to rapid intermittency
that prevents the growth of large scale structures. In our preferred scenario
the lack of extended radio emission in FR0s is due to their smaller jet Lorentz
$\Gamma$ factor with respect to FRIs, causing possible instabilities and their
premature disruption.[abridged]
