  We investigate the high-frequency radio spectra of twenty low-luminosity
active galactic nuclei (LLAGNs) with compact radio cores. Our millimetre survey
with the Nobeyama Millimetre Array (NMA) and analyses of submillimetre archival
data that had been obtained with the Submillimetre Common User Bolometer Array
(SCUBA) on the James Clerk Maxwell Telescope (JCMT) reveal the following
properties. At least half of the LLAGNs show inverted spectra between 15 and 96
GHz; we use published data at 15 GHz with the Very Large Array (VLA) in a
0.15-arcsec resolution and our measurements at 96 GHz with the NMA in a
7-arcsec resolution. The inverted spectra are not artificially made due to
their unmatched beam sizes, because of little diffuse contamination from dust,
H II regions, or extended jets in these LLAGNs. Such high-frequency inverted
spectra are apparently consistent with a `submillimetre bump', which is
predicted by an advection-dominated accretion flow (ADAF) model. We find a
strong correlation between the high-frequency spectral index and low-frequency
core power measured with very-long-baseline-interferometry (VLBI) instruments.
The inverted spectra were found exclusively in low-core-power sources, while
steep spectra were in high-core-power ones with prominent pc-scale jets. This
suggests that the ADAF and nonthermal jets may coexists. The flux ratios
between disc and jet seem to be different from LLAGN to LLAGN; disc components
can be seen in nuclear radio spectra only if the jets are faint.
