The solution of the Kato problem for degenerate elliptic operators with Gaussian bounds
Abstract
We prove the Kato conjecture for degenerate elliptic operators in Rn. More precisely, we consider the divergence form operator Lw = -1/w div (wA) grad, where w is a Muckenhoupt A2 weight and A is a complex valued n x n matrix which is bounded and uniformly elliptic. We show that if the associated semigroup satisfies Gaussian upper bounds, then the Kato square root estimate holds.
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