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The solution of Kato’s conjecture (after Auscher, Hofmann, Lacey, McIntosh and Tchamitchian). (English) Zbl 1213.35196

Journées “Équations aux dérivées partielles”, Plestin-les-Grèves, France, 5 au 8 juin 2001. Exposés Nos. I-XIV. Nantes: Université de Nantes (ISBN 2-86939-169-2/pbk). Exp. No. 14, 14 p. (2001).
Summary: Kato’s conjecture, stating that the domain of the square root of any accretive operator \(L=-\mathrm{div}(A\nabla)\) with bounded measurable coefficients in \(\mathbb{R}^n\) is the Sobolev space \(H^1(\mathbb{R}^n)\), i.e. the domain of the underlying sesquilinear form, has recently been obtained by P. Auscher, S.  Hofmann, M. Lacey, Michael, A. McIntosh and the author [Ann. Math. (2) 156, No. 2, 633–654 (2002; Zbl 1128.35316)]. These notes present the result and explain the strategy of proof.
For the entire collection see [Zbl 0990.00046].

MSC:

35J15 Second-order elliptic equations
47A60 Functional calculus for linear operators
42B25 Maximal functions, Littlewood-Paley theory

Citations:

Zbl 1128.35316
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