The Sloan Digital Sky Survey now extends over a large enough region that galaxies in low density environments can be detected .
Rojas et al .
have developed a technique to extract more than 1000 void galaxies with \delta \rho / \rho < -0.6 on scales r > 7 h ^ { -1 } Mpc from the SDSS .
In this paper , we present the luminosity function of these galaxies and compare it to that of galaxies at higher densities .
We obtain a measurement of the void galaxy luminosity function over the range -21.5 < M _ { r } ^ { * } < -14.5 in the SDSS r-band .
The void galaxy luminosity function ( LF ) is well fit by a Schechter function with values of \Phi ^ { * } = ( 0.19 \pm 0.04 ) \times 0.01 h ^ { 3 } Mpc ^ { -3 } , M _ { r } ^ { * } - 5log h = -19.74 \pm 0.11 and \alpha = -1.18 \pm 0.13 , where as the LF of the wall galaxy has Schechter function parameters \Phi ^ { * } = ( 1.42 \pm 0.03 ) \times 0.01 h ^ { 3 } Mpc ^ { -3 } , M _ { r } ^ { * } - 5log h = -20.62 \pm 0.08 and \alpha = -1.19 \pm 0.07 .
The fainter value of M _ { r } ^ { * } is consistent with the work of Rojas et al .
who found that void galaxies were fainter than galaxies at higher densities but the value of \alpha is very similar to that of galaxies at higher densities .
To investigate this further , the LF of wall and void galaxies as a function of density is considered .
Only the wall galaxies in the highest density regions have a shallower faint end slope .
The LF of the void galaxies is also compared to the LF of the wall galaxies with and without similar properties to the void galaxies ( color , Sersic index and strength of H \alpha emission ) .
The LF of the bluest , Sersic index n < 2 and EW ( H \alpha ) > 5 \AA wall galaxies is very similar in shape to that of the void galaxies , with only slightly brighter M _ { r } ^ { * } values and similar values of \alpha .
The LFs of the red , high Sersic index , low EW ( H \alpha ) wall galaxies have a much shallower slope and brighter M _ { r } ^ { * } values .
The value of \alpha \approx - 1.2 found from the void galaxy LF is shallower that that found from CDM models , suggesting that voids are not filled with a large population of dwarf galaxies .