Strict power concavity of a convolution

We give a sufficient condition for the strict parabolic power concavity of the convolution in space variable of a function defined on R-n x (0, +infinity) and a function defined on R-n. Since the strict parabolic power concavity of a function defined on R-n x (0, +infinity) naturally implies the strict power concavity of a function defined on R-n, our sufficient condition implies the strict power concavity of the convolution of two functions defined on R-n. As applications, we show the strict parabolic power concavity and strict power concavity in space variable of the Gauss-Weierstrass integral and the Poisson integral for the upper half-space.