Conjecture de Kato sur les ouverts de R.

Autores: Pascal Auscher, Ph. Tchamitchian
Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 8, Nº 2, 1992, págs. 149-199
Idioma: francés
DOI: 10.4171/rmi/121
Títulos paralelos:
- Kato's conjecture on open sets of R.
- Conjetura de Kato sobre los abiertos de R
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Resumen
- 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 = - d/dx a(x) 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).