We show that on a starshaped domain
Ω
\Omega
in
C
n
{\operatorname {C} ^n}
(actually on a somewhat larger, biholomorphically invariant class) the
L
p
{\mathcal {L}^p}
-Sobolev spaces of analytic functions form an interpolation scale for both the real and complex methods, for each
p
,
0
>
p
⩽
∞
p,\;0 > p \leqslant \infty
. The case
p
=
∞
p = \infty
gives the Lipschitz scale; here the functor
(
,
)
[
θ
]
{(,)^{[\theta ]}}
has to be considered (rather than
(
,
)
[
θ
]
{(,)_{[\theta ]}}
).