The solution of Kato's conjecture (after Auscher, Hofmann, Lacey, McIntosh and Tchamitchian)

Tchamitchian, Philippe

Journées équations aux dérivées partielles (2001), article no. 14, 14 p.

Kato’s conjecture, stating that the domain of the square root of any accretive operator $L=-div\left(A\nabla \right)$ with bounded measurable coefficients in ${ℝ}^n$ is the Sobolev space $H^1\left({ℝ}^n\right)$, i.e. the domain of the underlying sesquilinear form, has recently been obtained by Auscher, Hofmann, Lacey, McIntosh and the author. These notes present the result and explain the strategy of proof.

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