How to determine the class of a pseudo-homogeneous kernel that depend on a diagonal matrice

Question

Let $D$ be a $3\times3$ diagonal real matrice and denote by $|\cdot|$ the euclidian norm in $\mathbb{R}^3$.
I want to find the class of the following singular kernel: $$ \frac{1}{|x-y|}-\frac{1}{|D(x-y)|},\; x,y\in\mathbb{R}^3, x\neq y $$

Thank you.