Hard - X-rays selected Active Galactic Nuclei. I. A radio view at
  high-frequencies
  A thorough study of radio emission in Active Galactic Nuclei (AGN) is of
fundamental importance to understand the physical mechanisms responsible for
the emission and the interplay between accretion and ejection processes. High
frequency radio observations can target the nuclear contribution of smaller
emitting regions and are less affected by absorption. We present JVLA 22 and 45
GHz observations of 16 nearby (0.003$\le$z$\le$0.3) hard - X-rays selected AGN
at the (sub)-kpc scale with tens uJy beam$^{-1}$ sensitivity. We detected 15/16
sources, with flux densities ranging from hundreds uJy beam$^{-1}$ to tens Jy
(specific luminosities from $\sim$10$^{20}$ to $\sim$10$^{25}\,W\,Hz^{-1}$ at
22 GHz). All detected sources host a compact core, with 8 being core-dominated
at either frequencies, the others exhibiting also extended structures. Spectral
indices range from steep to flat/inverted. We interpret this evidence as either
due to a core+jet system (6/15), a core accompanied by surrounding star
formation (1/15), to a jet oriented close to the line of sight (3/15), to
emission from a corona or the base of a jet (1/15), although there might be
degeneracies between different processes. Four sources require more data to
shed light on their nature. We conclude that, at these frequencies, extended,
optically-thin components are present together with the flat-spectrum core. The
${L_R}/{L_X}\sim10^{-5}$ relation is roughly followed, indicating a possible
contribution to radio emission from a hot corona. A weakly significant
correlation between radio core (22 and 45 GHz) and X-rays luminosities is
discussed in the light of an accretion-ejection framework.
