  We investigate the relation between star formation (SF) and black hole
accretion luminosities, using a sample of 492 type-2 active galactic nuclei
(AGNs) at z < 0.22, which are detected in the far-infrared (FIR) surveys with
AKARI and Herschel. We adopt FIR luminosities at 90 and 100 um as SF
luminosities, assuming the proposed linear proportionality of star formation
rate with FIR luminosities. By estimating AGN luminosities from [OIII]5007 and
[OI]6300 emission lines, we find a positive linear trend between FIR and AGN
luminosities over a wide dynamical range. This result appears to be
inconsistent with the recent reports that low-luminosity AGNs show essentially
no correlation between FIR and X-ray luminosities, while the discrepancy is
likely due to the Malmquist and sample selection biases. By analyzing the
spectral energy distribution, we find that pure-AGN candidates, of which FIR
radiation is thought to be AGN-dominated, show significantly low-SF activities.
These AGNs hosted by low-SF galaxies are rare in our sample (~ 1%). However,
the low fraction of low-SF AGN is possibly due to observational limitations
since the recent FIR surveys are insufficient to examine the population of
high-luminosity AGNs hosted by low-SF galaxies.
