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 on an interval, when is a bounded and accretive function. We show for the latter situation that the domain of is spanned by an unconditional basis of wavelets with cancellation properties that compensate the action of the non-regular function .
Cite this article
Pascal Auscher, Philippe Tchamitchian, Conjecture de Kato sur les ouverts de . Rev. Mat. Iberoam. 8 (1992), no. 2, pp. 149–199DOI 10.4171/RMI/121