Recently, V. Cruz, J. Mateu and J. Orobitg have proved a T(1) theorem for the Beurling transform in the complex plane. It asserts that given \( 0< s \leq 1 \), \( 1 < p < \infty \) with \(sp>2\) and a Lipschitz domain \(\Omega\subset \mathbb{C}\), the Beurling transform \(Bf=- {\rm p.v.}\frac1{\pi z^2}*f\) is bounded in the Sobolev space \(W^{s,p}(\Omega)\) if and only if \(B\chi_\Omega\in W^{s,p}(\Omega)\).

In this paper we obtain a generalized version of the former result valid for any \(s\in \mathbb{N}\) and for a larger family of Calderón-Zygmund operators in any ambient space \(\mathbb{R}^d\) as long as \(p>d\). In that case we need to check the boundedness not only over the characteristic function of the domain, but over a finite collection of polynomials restricted to the domain. Finally we find a sufficient condition in terms of Carleson measures for \(p\leq d\). In the particular case \(s=1\), this condition is in fact necessary, which yields a complete characterization.