  We aim to study the optical and near-infrared linear polarimetric properties
of a sample of young M7-L7 dwarfs ($\approx$1-500 Myr) with spectroscopic
signatures of low- and intermediate-gravity atmospheres. We collected optical
($RIZ$) and near-infrared ($YJHK_{\rm s}$) linear polarimetry images on various
time scales from $\sim$0.2 h to months. Linear polarization degrees in the
interval 0-1.5\% ($I$- and $J$-bands) were measured with accuracies ranging
from $\pm$0.1 $\%$ to $\pm$0.9 $\%$ depending on the observing filter and the
target brightness. We found that the young field dwarfs in our sample show
similar polarimetric degrees at both $I$- and $J$-bands, and that there is no
obvious trend with the spectral type. The two Taurus sources in our sample show
intense levels of $J$-band linear polarization probably due to surrounding
disks. By compiling data from the literature for high-gravity M7-L7 dwarfs with
likely ages $\ge$500 Myr, we did not observe any apparent difference in the
linear polarimetry intensity between the young and old samples that could be
ascribed to differing atmospheric gravities. Polarimetric variability with peak
to peak amplitudes up to 1.5 $\%$ is detected on scales of about a rotation in
two out of four targets that were monitored over several hours. Long-term
polarimetric variability is also detected in nearly all dwarfs of the sample
with data spanning months to years.
