JournalsrmiVol. 8, No. 2pp. 149–199

Conjecture de Kato sur les ouverts de R\mathbb R

  • Pascal Auscher

    Université de Paris-Sud, Orsay, France
  • Philippe Tchamitchian

    CNRS Luminy, Marseille, France
Conjecture de Kato sur les ouverts de $\mathbb R$ cover
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Abstract

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=ddxa(x)ddxT = –\frac{d}{dx}a(x)\frac{d}{dx} on an interval, when a(x)a(x) is a bounded and accretive function. We show for the latter situation that the domain of TT is spanned by an unconditional basis of wavelets with cancellation properties that compensate the action of the non-regular function a(x)a( x).

Cite this article

Pascal Auscher, Philippe Tchamitchian, Conjecture de Kato sur les ouverts de R\mathbb R. Rev. Mat. Iberoam. 8 (1992), no. 2, pp. 149–199

DOI 10.4171/RMI/121