The author proves that the estimate of the norm of the operator \[ T_ Af(x)=\lim_{\epsilon \to +0}\int_{| x-y| >\epsilon}[x- y+i(A(x)-A(y))]^{-1} f(y)dy \] established by T. Murai is optimal by showing that \(\| TA\|_{L^ 2(R),L^ 2(R)}\geq M^{1/2}/10\) if \(\| A'\|_{\infty}\leq M\), where A is a Lipschitz function on R. The idea of the proof is to use the Cantor set of the complex plane known under the name “Garnette’s example”.