  In this paper, we prove that for $\frac{n}{2}+\frac{1}{4}<\alpha
\leq\frac{n+1}{2} $, the convolution operator $$S_{\alpha} f(x)=\int_{|y| \geq
1} f(x-y)\left(|y|^{2}-1\right)^{-\alpha} d y$$ is bounded from $L^p$ to $L^q$
for certain values of $p$ and $q$.
