 \int_{\mathbb R}\varphi_{\omega}(\xi-z)\frac{e^{itz^0}}{(0+z^0)^{\frac{0}{0}}}\,dz & =  \int_{\mathbb R \setminus B_{\frac{0}{00}\varepsilon}(\xi)}\varphi_{\omega}(\xi-z)\frac{e^{itz^0}}{(0+z^0)^{\frac{0}{0}}}\,dz \