Revista Matemática Iberoamericana

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Volume 8, Issue 2, 1992, pp. 149–199
DOI: 10.4171/RMI/121

Published online: 1992-08-31

Conjecture de Kato sur les ouverts de $\mathbb R$

Pascal Auscher[1] and Philippe Tchamitchian[2]

(1) Université de Paris-Sud, Orsay, France
(2) CNRS Luminy, Marseille, France

We prove Kato's conjecture for second order elliptic differential operators on an open set in dimension 1 with arbitrary boundary conditions. The general case reduces to studying the operator $T = –\frac{d}{dx}a(x)\frac{d}{dx}$ on an interval, when $a(x)$ is a bounded and accretive function. We show for the latter situation that the domain of $T$ is spanned by an unconditional basis of wavelets with cancellation properties that compensate the action of the non-regular function $a( x)$.

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Auscher Pascal, Tchamitchian Philippe: Conjecture de Kato sur les ouverts de $\mathbb R$. Rev. Mat. Iberoamericana 8 (1992), 149-199. doi: 10.4171/RMI/121