  We study interaction effects on the topological crystalline insulators
protected by time-reversal ($T$) and reflection symmetry ($R$) in two and three
spatial dimensions. From the stability analysis of the edge states with
bosonization, we find that the classification of the two-dimensional SPT phases
protected by $Z_2\times[\mbox{U(1)}\rtimes T]$ symmetry is reduced from
$\mathbb{Z}$ to $\mathbb{Z}_4$ by interactions, where the $Z_2$ symmetry
denotes the reflection whose mirror plane is the two-dimensional plane itself.
By extending the approach recently proposed by Isobe and Fu, we show that the
classification of the three-dimensional SPT phases (i.e., topological
crystalline insulators) protected by $R\times[\mbox{U(1)}\rtimes T]$ symmetry
is reduced from $\mathbb{Z}$ to $\mathbb{Z}_8$ by interactions.
