Abstract
Abstract
Let
D
= {z : |z| < 1} be the unit disk in the complex plane C, Φ :
D
→ C is a analytic map. We study the multiplication operator M
Φ
on the logarithmic weighted BMOA space
B
M
O
A
log
=
{
g
∈
H
(
D
)
:
sup
a
∈
D
(
log
2
1
−
|
a
|
2
)
2
∫
D
|
g
′
(
z
)
|
2
(
1
−
|
φ
a
(
z
)
|
2
)
d
m
(
z
)
<
∞
}
. We obtain that a sufficient condition for the operator M
Φ
to be a bounded operator on BMOA
log. We also get that another necessary condition for the operator M
Φ
to be bounded on BMOA
log.
Subject
General Physics and Astronomy
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