  The Riesz transform of $u$ : $\mathcal{S}(\mathbb{R}^n) \rightarrow
\mathcal{S'}(\mathbb{R}^n)$ is defined as a convolution by a singular kernel,
and can be conveniently expressed using the Fourier Transform and a simple
multiplier. We extend this analysis to higher order Riesz transforms, i.e. some
type of singular integrals that contain tensorial polyadic kernels and define
an integral transform for functions $\mathcal{S}(\mathbb{R}^n) \rightarrow
\mathcal{S'}(\mathbb{R}^{ n \times n \times \dots n})$. We show that the
transformed kernel is also a polyadic tensor, and propose a general method to
compute explicitely the Fourier mutliplier. Analytical results are given, as
well as a recursive algorithm, to compute the coefficients of the transformed
kernel. We compare the result to direct numerical evaluation, and discuss the
case $n=2$, with application to image analysis.
