A³COSMOS (red boxes and black circles) + Herschel (black triangles) luminosity function. The dark-red lines and shaded areas are the best fit obtained by using all the LF points from different z-bins together. The redshift ranges are reported in the upper-right corner of each subplot, while the luminosity bins are centered at each 0.25 dex, with a width of 0.5 dex (overlapping bins). The black vertical dashed lines represent the completeness limit of the L_IR. The orange dashed, purple dotted, and green dashed lines are the best-fit LFs obtained by Gruppioni et al. (2013, 2020), Magnelli et al. (2013).