  The radio luminosity functions (RLFs) of active galactic nuclei (AGNs) are
traditionally measured based on total emission, which doesn't reflect the
current activity of the central black hole. The increasing interest in compact
radio cores of AGNs requires determination of the RLF based on core emission
(i.e., core RLF). In this work we have established a large sample (totaling
1207) of radio-loud AGNs, mainly consisting of radio galaxies (RGs) and
steep-spectrum radio quasars (SSRQs). Based on the sample, we explore the
relationship between core luminosity ($L_c$) and total luminosity ($L_t$) via a
powerful statistical tool called "Copula". The conditional probability
distribution $p(\log L_{c} \mid \log L_{t})$ is obtained. We derive the core
RLF as a convolution of $p(\log L_{c} \mid \log L_{t})$ with the total RLF
which was determined by previous work. We relate the separate RG and SSRQ core
RLFs via a relativistic beaming model and find that SSRQs have an average
Lorentz factor of $\gamma=9.84_{-2.50}^{+3.61}$, and that most are seen within
$8^{\circ} \lesssim \theta \lesssim 45^{\circ}$ of the jet axis. Compared with
the total RLF which is mainly contributed by extended emission, the core RLF
shows a very weak luminosity-dependent evolution, with the number density
peaking around $z\thicksim 0.8$ for all luminosities. Differences between core
and total RLFs can be explained in a framework involving a combination of
density and luminosity evolutions where the cores have significantly weaker
luminosity evolution than the extended emission.
