Let
D
D
be a Jordan domain in the complex plane with rectifiable boundary
C
C
. Let
A
q
(
D
)
{A_q}(D)
denote the Bers space with norm
|
|
|
|
q
||\;|{|_q}
. We prove that if
f
∈
A
q
(
D
)
,
2
>
q
>
∞
f \in {A_q}(D),2 > q > \infty
, then there exist functions
s
n
(
z
)
=
Σ
k
=
1
n
1
/
(
z
−
z
n
,
k
)
,
z
n
,
k
∈
C
for
k
=
1
,
⋯
,
n
{s_n}(z) = \Sigma _{k = 1}^n1/(z - {z_{n,k}}),\;{z_{n,k}} \in C{\text { for }}k = 1, \cdots ,n
, such that
|
|
s
n
−
f
|
|
q
→
0
||{s_n} - f|{|_q} \to 0
. This result does not hold for
1
>
q
≦
2
1 > q \leqq 2
even when
D
D
is a disc.