Strict power concavity of a convolution

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