We consider one series of unitarizable representations, the cohomological induced modules
A
q
(
λ
)
A_{\mathfrak {q}}(\lambda )
with dominant regular infinitesimal character. The minimal
K
K
-type
(
τ
,
V
)
(\tau , V)
of
A
q
(
λ
)
A_{\mathfrak {q}}(\lambda )
determines a homogeneous vector bundle
V
τ
⟶
G
/
K
V_{\tau } \longrightarrow G/K
. The derived functor modules can be realized on the solution space of a first order differential operator
D
l
λ
\mathcal {D}_{\mathfrak {l}}^{\lambda }
on
V
τ
V_{\tau }
. Barchini, Knapp and Zierau gave an explicit integral map
S
\mathcal {S}
from the derived functor module, realized in the Langlands classification, into the space of smooth sections of the vector bundle
V
τ
⟶
G
/
K
V_{\tau } \longrightarrow G/K
. In this paper we study the asymptotic behavior of elements in the image of
S
\mathcal {S}
. We obtain a factorization of the standard intertwining opeartors into the composition of the Szegö map
S
\mathcal {S}
and a passage to boundary values.