Connection between generalized bessel potentials and solutions to the singular heat equation

In this paper, we consider a generalization of the Gauss-Weierstrass kernel, which is the solution of the singular heat equation and the integral corresponding to it. We study their properties. Further, we show that the generalized Bessel potential of a function integrable to the p-th degree with a power weight can be represented by an integral of a very simple form using the Gauss–Weierstrass kernel.