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On $L^p$ estimates for square roots of second order elliptic operators on $\mathbb{R}^n$
We prove that the square root of a uniformly complex elliptic operator L = -div(A∇) with bounded measurable coefficients in R n satisfies the estimate L 1/2 f p ∇f p for sup(1, 2n n+4ε) < p < 2n n-2 + ε, which is new for n ≥ 5 and …