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It asserts that given $0<s\\leq1$, $1<p<\\infty$ 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 $B\\chi_\\Omega\\in W^{s,p}(\\Omega)$.\n  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 Calder\\'on-Zygmund operators in any ambient space $\\mathbb{R}^d$ as long as $p>d$. 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