$L^2$-boundedness of a singular integral operator

In this paper we study a singular integral operator $T$ with rough kernel. This operator has singularity along sets of the form $\{x=Q(|y|)y'\}$, where $Q(t)$ is a polynomial satisfying $Q(0)=0$. We prove that $T$ is a bounded operator in the space $L^2(R^n)$, $n\ge 2$, and this bound is independent of the coefficients of $Q(t)$.

We also obtain certain Hardy type inequalities related to this operator.