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.

Thanks,

Hollywood