This seems to be the correct place for complex analysis. Here's the problem I'm working on:
Let be the disk , and let be the unit disk . Let be an analytic function on .
(a) Let . Show that for any , , we have:
(b) Show that if , then:
(c) Let be a family of analytic functions on for which there exists such that:
Show that is a normal family.
For (c), a normal family is one in which every sequence in has a subsequence that converges uniformly on compact subsets.
Unless I'm missing something, (b) follows from (a) by just taking the absolute value:
and since this must be true for all , taking the limit as goes to gives
I'm still lost on (a) and (c), though.