Let W_p⁽²⁾ be the Sobolev space of probability density functions f(X) whose first derivative is absolutely continuous and whose second derivative is in L_p(- ∞ ,+ ∞), for p ∈ [1, + ∞]. Using an upper bound to the mean square error for a fixed X E [f(X) - f_n(X)0]², found by G. Wahba, where f_n(X) is the Parzen Kernel-type estimate of f(X), we find the finite support Kernel function K(X) that minimizes the said upper bound. The optimal Kernel funciton is: K(y) = (1+a^-1) (2T)^-1 [1-T^-a |y|^a], for |y|<T where [-T,T] is the support interval, and a=2-p^-1.