We investigate the effects of the observed UV background radiation on
galaxy formation. Photoionization by UV radiation decreases the coolin
g rate of the gas in halos, so that objects with only large density co
ntrasts can self-shield against the background radiation, thereby allo
wing the shielded neutral cores to cool and form stars. In the context
of the CDM model, we use the criterion that self-shielding is essenti
al for star formation to calculate the mass function of galaxies based
on both Press-Schechter and the peaks formalisms. The ionizing UV rad
iation causes inhibition of galaxy formation-we show the decrease in t
he number density of the galaxies quantitatively. We also find that th
e merging in general is made inefficient by the UV photons through pho
toionization of the gas in the bigger system into which small objects
are incorporated. The latter means that, in a merging-dominated region
, where the number density at the low-mass end (M(b) less than or simi
lar to 10(10) Mm.) is usually expected to decrease with time, the tren
d is reversed (the number of low-mass galaxies is greater at lower red
shifts z) due to the decreasing UV flux with time after z similar to 2
. We further discuss the implication of our results for the number cou
nts of galaxies and possible evolution of the luminosity function of t
he galaxies.