In a paper by Calderon and Zygmund some properties of a certain kind of singular integral are established, and these results are applied to particular fundamental solutions arising in partial differential equations. Jones has considered another class of singular integrals which has application to fundamental solutions of the heat equation. More generally the kernels considered by Jones arise from parabolic differential equations with constant coefficient. This thesis considers a kernel which is a generalization of the kernel treated by Jones, and it has mean value and homogenity properties analogous to those in Jones's paper.