  We give a sufficient condition for the strict parabolic power concavity of
the convolution in space variable of a function defined on $\mathbb{R}^n \times
(0,+\infty)$ and a function defined on $\mathbb{R}^n$. Since the strict
parabolic power concavity of a function defined on $\mathbb{R}^n \times
(0,+\infty)$ naturally implies the strict power concavity of a function defined
on $\mathbb{R}^n$, our sufficient condition implies the strict power concavity
of the convolution of two functions defined on $\mathbb{R}^n$. As applications,
we show the strict parabolic power concavity and strict power concavity in
space variable of the Gauss--Weierstass integral and the Poisson integral for
the upper half-space.
