Norm and Essential Norm of Composition Operator on Bergman Space

Let D be the unit disk, $A^p(D)$ be the Bergman space in D and $\varphi$ be an analytic self-map of D. The composition operator $C_\varphi$ is defined as $$(C_\varphi f)(z)=f(\varphi(z)) .$$ Then the property of KSP of the composition operator on $A^p(D)$ is investigated, and the norm and the essential norm of some composition operators on Bergman spaces on D are calculated.