Assume that
\Omega
Ω
is a strongly convex domain, balanced with boundary of class
C^{1}
C
1
. Fix number
p \geq 1
p
≥
1
. For any set
E
E
which is circular and of type
G_{\delta}
G
δ
in
\partial\Omega
∂
Ω
we find a holomorphic function
f\in \mathbb{O}(\Omega)
f
∈
O
(
Ω
)
such that
E=E_{\Omega}^{p}(f)=\left\{ z\in \partial \Omega: \:\int_{|\lambda| <1} \left|f(\lambda z)\right|^{p}d\mathfrak{L}^{2}(\lambda)=\infty\right\}.
E
=
E
Ω
p
(
f
)
=
{
z
∈
∂
Ω
:
∫
∣
λ
∣
<
1
∣
f
(
λ
z
)
∣
p
d
L
2
(
λ
)
=
∞
}
.