Continuity of Calderón-Zygmund Operators on the Space BMO

Résumé

David and Journé discovered a criterion for the continuity on L2 of Calder´on- Zygmund operators defined by singular integrals. In their approach the distributional kernel of the given operator is locally H¨older continuous outside the diagonal. The aim of this paper is to prove a David-Journ´e theorem where this smoothness assumption is replaced by a weaker one. Our approach strongly relies on an algorithm developed by Beylkin, Coifman, and Rokhlin.