By a result of B. Dahlberg, the composition operators
T
H
f
=
H
∘
f
{T_H}f = H \circ f
need not be bounded on some of the Sobolev spaces (or spaces of Bessel potentials) even for very smooth functions
H
=
H
(
t
)
,
H
(
0
)
=
0
H = H\left ( t \right ),H\left ( 0 \right ) = 0
, unless of course,
H
(
t
)
=
c
t
H\left ( t \right ) = ct
. In this note a natural domain is found for
T
H
{T_H}
that is, in a sense, maximal and on which the
{
T
H
}
\left \{ {{T_H}} \right \}
form an algebra of bounded operators. Here the functions
H
(
t
)
H\left ( t \right )
need not be bounded though they are required to have a sufficient number of bounded derivatives.