$$\mbox{Define}\quadG(x,y)=\frac{Ci\left(\gamma(x-y_c)\right)Ai\left(\gamma(y-y_c)\right)}{\epsilon\gamma},$$
- where $y>x,$$y_c$ is a complex number such that $\Re(y_c)>0,$
- $\epsilon$ is a pure imaginary number such that $\Im(\epsilon)>0,$
- $\gamma$ is a complex number such that $0<\gamma<\pi/3,$
- and $\epsilon\gamma^3=\lambda,$ in which $\lambda$ is a fixed complex number independent with $\epsilon$ and $\gamma.$
I want to prove the following inequality$$\int_{x}^{+\infty}|G(x,y)|dy\leq C\min\left(|x-y_c|^{-1},\gamma\right),$$where $C$ is some constant independent with $\gamma$.
Does anyone know how to get the above inequality ?. Thanks a lot.