Lemma 3.6
(Borel-Caratheodory Theorem)
.
Assuming that:
0
<
r
<
R
f
analytic in
B
(
0
,
R
)
¯
, with
f
(
0
)
=
0
Then
sup
|
z
|
≤
r
|
f
(
z
)
|
≤
2
r
R
−
r
sup
|
z
|
=
R
Re
(
f
(
z
)
)
.