Let $,T^{j,k}_{N}:L^{p}(B),
ightarrow,L^{q}([0,1]),$ be the oscillatory integral operators defined by $;displaystyle T^{j,k}_{N}f(s):=int_{B}
,f(x),e^{imath N{|x|}^{j}s^{k}},dx,quad (j,k)in{1,2}^{2},,$ where $,B,$ is the unit ball in ${mathbb{R}}^{n},$ and $,N,>>1.$ We compare the asymptotic behaviour as $,N
ightarrow +infty,$ of the operator norms $,parallel T^{j,k}_{N} parallel_{L^{p}(B)
ightarrow L^{q}([0,1])},$
for all $,p,,qin [1,+infty].,$ We prove that, except for the dimension $n=1,,$ this asymptotic behaviour depends on the linearity or quadraticity of the phase in $s$ only. We are led to this problem by an observation on inhomogeneous Strichartz estimates for the Schr"{o}dinger equation.