The Planck Early Release Compact Source Catalog (ERCSC) has offered the first opportunity to accurately determine the luminosity function of dusty galaxies in the very local Universe (i.e. distances <~ 100 Mpc), at several (sub-)millimetre wavelength
s, using blindly selected samples of low redshift sources, unaffected by cosmological evolution. This project, however, requires careful consideration of a variety of issues including the choice of the appropriate flux density measurement, the separation of dusty galaxies from radio sources and from Galactic sources, the correction for the CO emission, the effect of density inhomogeneities, and more. We present estimates of the local luminosity functions at 857 GHz (350 microns), 545 GHz (550 microns) and 353 GHz (850 microns) extending across the characteristic luminosity L_star, and a preliminary estimate over a limited luminosity range at 217 GHz (1382 microns). At 850 microns and for luminosities L >~ L_star our results agree with previous estimates, derived from the SCUBA Local Universe Galaxy Survey (SLUGS), but are higher than the latter at L <~ L_star. We also find good agreement with estimates at 350 and 500 microns based on preliminary Herschel survey data.
