### The higher order Riesz transform for Gaussian measure need not be of weak type (1,1)

The purpose of this paper is to prove that the higher order Riesz transform for Gaussian measure associated with the Ornstein-Uhlenbeck differential operator $L:={d}^{2}/d{x}^{2}-2xd/dx$, x ∈ ℝ, need not be of weak type (1,1). A function in ${L}^{1}\left(d\gamma \right)$, where dγ is the Gaussian measure, is given such that the distribution function of the higher order Riesz transform decays more slowly than C/λ.