We present the results of Karl G. Jansky Very Large Array (VLA) observations to study the properties of FR0 radio galaxies, the compact radio sources associated with early-type galaxies which represent the bulk of the local radio-loud AGN population. We obtained A-array observations at 1.5, 4.5, and 7.5 GHz for 18 FR0s from the FR0CAT sample: these are sources at $z<0.05$, unresolved in the FIRST images and spectroscopically classified as low excitation galaxies (LEG). Although we reach an angular resolution of $sim$0.3 arcsec, the majority of the 18 FR0s is still unresolved. Only four objects show extended emission. Six have steep radio spectra, 11 are flat cores, while one shows an inverted spectrum. We find that 1) the ratio between core and total emission in FR0s is $sim$30 times higher than in FRI and 2) FR0s share the same properties with FRIs from the nuclear and host point of view. FR0s differ from FRIs only for the paucity of extended radio emission. Different scenarios were investigated: 1) the possibility that all FR0s are young sources eventually evolving into extended sources is ruled out by the distribution of radio sizes; 2) similarly, a time-dependent scenario, where a variation of accretion or jet launching prevents the formation of large-scales radio structures, appears to be rather implausible due to the large abundance of sub-kpc objects 3) a scenario in which FR0s are produced by mildly relativistic jets is consistent with the data but requires observations of a larger sample to be properly tested.