  Searching for Earth-sized planets in data from Kepler's extended mission (K2)
is a niche that still remains to be fully exploited. The TFAW survey is an
ongoing project that aims to re-analyze all light curves in K2 C1-C8 and
C12-C18 campaigns with a wavelet-based detrending and denoising method, and the
period search algorithm TLS to search for new transit candidates not detected
in previous works. We have analyzed a first subset of 24 candidate planetary
systems around relatively faint host stars (10.9 < $K_{p}$ < 15.4) to allow for
follow-up speckle imaging observations. Using VESPA and TRICERATOPS, we
statistically validate six candidates orbiting four unique host stars by
obtaining false-positive probabilities smaller than 1% with both methods. We
also present 13 vetted planet candidates that might benefit from other, more
precise follow-up observations. All of these planets are sub-Neptune-sized,
with two validated planets and three candidates with sub-Earth sizes, and have
orbital periods between 0.81 and 23.98 days. Some interesting systems include
two ultra-short-period planets, three multi-planetary systems, three
sub-Neptunes that appear to be within the small planet Radius Gap, and two
validated and one candidate sub-Earths (EPIC 210706310, EPIC 210768568, and
EPIC 246078343) orbiting metal-poor stars.

Earth and Planetary Astrophysics