Suppose a function h is holomorphic in the open unit disk D = {z ∈ C: |z| < 1} and satisfies |h(z)| ≤ 1 for all z in D, but h(0) ≠ 0. Which of the following statements is correct given Schwartz's Lemma?
1
|h(z)| ≤ |z| for all z in D
2
The Schwarz Lemma is applicable to function h
3
|h'(0)| ≤ 1
4
h(z) must be a rotation