A note on Singular integral

In this paper, we prove that for $\frac{n}{2}+\frac{1}{4}<\alpha \leq\frac{n+1}{2} $,theconvolutionoperator$$S_{\alpha} f(x)=\int_{|y| \geq 1} f(x-y)\left(|y|^{2}-1\right)^{-\alpha} d y$$isboundedfrom$L^p$to$L^q$forcertainvaluesof$p$and$q$.