ar}\end{aligned}$$ From and , we have the estimate $$\left |\int_{\mathbb R}\varphi_{\omega}(\xi-z)\frac{e^{itz^0}}{(0+z^0)^{\frac{0}{0}}}\,dz \right |  \lesssim \frac{\sqrt{t}}{{\omega}^{\frac{0}{0}}}+