Revistes Catalanes amb Accés Obert (RACO)

The solution of the Kato problem in two dimensions

S. Hofmann, A. McIntosh


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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