$L^p$ boundness of Oscillatory singular integral with Calderón Type Commutators

In the paper, we study a kind of Oscillatory singular integral operator with Calderón Type Commutators $T_{P,K,A}$ defined by $$T_{P,K,A}f(x)=\text{ p.v.}{\int }_{{\mathbb{R}}^n}f(y)\frac{K(x-y)}{\mathrm{\mid }x-y\mathrm{\mid }}(A(x)-A(y)-\mathrm{\nabla }A(y))(x-y)e^{iP(x-y)}dy,$$ where $P(t)$ is a real polynomial on $\mathbb{R},$ and $K$ is a function on ${\mathbb{R}}^n,$ satisfies the vanishing moment and $CZ(\delta )$ conditions. Under these conditions, we show that $T_{P,K,A}$ is bounded on $L^p({\mathbb{R}}^n)$ with uniform boundedness, which improve and extend the previous result.