  The world-sheet quantum conformal invariance can be realized in the presence
of the conformal factor $F$, by inclusion of Liouville term. In the background
with linear dilaton field, $\Phi(x)=\Phi_0+a_\mu x^\mu$, the field $F$ becomes
a new noncommutative variable. Therefore, it is natural to extend space-time
with a new coordinate, $F$, in order to unify expressions for noncommutativity
parameter $\Theta^{ij}$ of the space-time coordinates $x^i$, with the part
$\Theta^i$ connecting noncommutativity between coordinates $x^i$ and $F$. In
this way we solve the problems of Dp-brane noncommutativity in a more elegant
way. The technical advantage uses the fact that in the extended space-time the
action with dilaton field can be rewritten in dilaton free form. We use
canonical method and extend its application to the derivation of boundary
conditions. From requirement that Hamiltonian, as the time translation
generator, has well defined derivatives in the coordinates and momenta, we
obtain boundary conditions directly in the canonical form.
