  We study the properties and the origin of the radio emission in the most
luminous early-type galaxies (ETGs) in the nearby Universe (MK<-25, recession
velocity < 7,500 km/s) as seen by the 150 MHz Low-Frequency ARray (LOFAR)
observations. LOFAR images are available for 188 of these giant ETGs (gETGs)
and 146 (78%) of them are detected above a typical luminosity of ~10E21 W/Hz.
They show a large spread in power, reaching up to ~10E26 W/Hz. We confirm a
positive link between the stellar luminosity of gETGs and their median radio
power, the detection rate, and the fraction of extended sources. About
two-thirds (91) of the detected gETGs are unresolved, with sizes <4 kpc,
confirming the prevalence of compact radio sources in local sources. Forty-six
gETGs show extended emission on scales ranging from 4 to 340 kpc, at least 80%
of which have a FRI class morphology. Based on the morphology and spectral
index of the extended sources, ~30% of them might be remnant or restarted
sources but further studies are needed to confirm this. Optical spectroscopy
(available for 44 gETGs) indicates that for seven of them the nuclear gas is
ionized by young stars suggesting a contribution to their radio emission from
star forming regions. Their radio luminosities correspond to a star formation
rate (SFR) in the range 0.1-8 Msun/yr and a median specific SFR of 0.8x10E-12
yr-1. The gas flowing toward the center of gETGs can accrete onto the
supermassive black hole but also stall at larger radii and form new stars, an
indication that feedback does not completely quench star formation. The most
luminous gETGs (25 galaxies with MK < -25.8) are all detected at 150 MHz
however they are not all currently turned on: at least four of them are remnant
sources and at least one is likely powered by star formation.
