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This was begun by Cruz-Uribe and Rios who proved that given an operator $L_w=-w^{-1}{\\rm div}(A\\nabla)$, where $w\\in A_2$ and $A$ is a $w$-degenerate elliptic measure (i.e, $A=w\\,B$ with $B$ an $n\\times n$ bounded, complex-valued, uniformly elliptic matrix), then $L_w$ satisfies the weighted estimate $\\|\\sqrt{L_w}f\\|_{L^2(w)}\\approx\\|\\nabla f\\|_{L^2(w)}$. 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