The solution of the Kato problem in two dimensions
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We solve, in two dimensions, the "square root problem of Kato". That is, for $L\equiv -\operatorname{div} (A(x)\nabla)$, where $A(x)$ is a $2\times 2 $ accretive matrix of bounded measurable complex coefficients, we prove that $L^{1/2}\colon L^2_1(\mathbb{R}^2) \rightarrow L^2(\mathbb{R}^2)$.
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Hofmann, S.; and McIntosh, A. “The solution of the Kato problem in two dimensions”. Publicacions Matemàtiques, pp. 143-60, https://raco.cat/index.php/PublicacionsMatematiques/article/view/38034.
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