Bergman space of holomorphic functions on unit disc is closed in L^2 (unit disc)
Could you please help with the following question:
Let be the Bergman space of all holomorphic functions on the unit disc which also belong to . Let , and . Cauchy's Integral Formula gives:
By integrating this formula for , we are supposed to show that
where is the disc of radius with centre .
From this, we should deduce that
From this I know how to deduce that is closed in ; it's just the above calculations which confuse me.