Arcozzi, Rochberg, Sawyer and Wick obtained a characterization of the holomorphic functions
b
b
such that the Hankel type bilinear form
T
b
(
f
,
g
)
=
∫
D
(
I
+
R
)
(
f
g
)
(
z
)
(
I
+
R
)
b
(
z
)
¯
d
v
(
z
)
T_{b}(f,g)= \int _{{\mathbb D}}(I+R)(fg)(z) \overline {(I+R)b(z)}dv(z)
is bounded on
D
×
D
{\mathcal D}\times {\mathcal D}
, where
D
{\mathcal D}
is the Dirichlet space. In this paper we give an alternative proof of this characterization which tries to understand the similarity with the results of Maz
′
’
ya and Verbitsky relative to the Schrödinger forms on the Sobolev spaces
L
2
1
(
R
n
)
L_2^1(\mathbb {R}^n)
.