  Given a Lipschitz domain $D\subset \mathbb{R}^d,$ a Calder\'on-Zygmund
operator $T$ and a modulus of continuity $\omega(x),$ we solve a problem when
the restricted operator $T_Df=T(f\chi_D)\chi_D$ sends the Campanato space
$\mathcal{C}_\omega(D)$ into itself. The solution is a T1 type sufficient and
necessary condition for the characteristic function $\chi_D$ of $D$:
  $$(T\chi_D)\chi_D \in \mathcal{C}_{\tilde{\omega}}(D),$$ assumed
$\tilde{\omega}(x)= \omega(x)/\int_x^1 \omega(t)dt/t.$ To check the hypotheses
of T1 theorem we need extra restrictions on both the boundary of $D$ and the
operator $T.$ It is proved that the restricted Calder\'on-Zygmund operator
$T_D$ with the even kernel is bounded on $\mathcal{C}_\omega(D),$ provided $D$
be $C^{1,\tilde{\omega}}-$smooth domain. This result is sharp.
