The properties and luminosity function of extremely low luminosity   galaxies
  We examine a sample of low redshift (10 < d < 150 Mpc) galaxies including galaxies with r-band absolute magnitudes as faint as -12.5 (for h=1), selected from the Sloan Digital Sky Survey Data Release 2 (SDSS). The sample is unique in containing galaxies of extremely low luminosities in a wide range of environments, selected with uniform and well-understood criteria. We present the luminosity function as well as the broad-band properties of low luminosity galaxies in this sample. A Schechter function is an insufficient parameterization of the r-band luminosity function; there is an upturn in the slope at low luminosities. The resulting slope at low luminosities in this sample is around -1.3. However, we almost certainly miss a large number of galaxies at very low luminosities due to low surface brightness selection effects, and we estimate that the true low luminosity slope may be as steep or steeper than -1.5. The results here are consistent with previous SDSS results and, in the g-band, roughly consistent with the results of the Two degree Field Galaxy Redshift Survey. Extremely low luminosity galaxies are predominantly blue, low surface brightness, exponential disks. 
Michael R. Blanton, Robert H. Lupton, David J. Schlegel, Michael A.   Strauss, J. Brinkmann, Masataka Fukugita, and Jon Loveday