Full paper in PDF format:
$%Q. Yang, Continuity of Calderón-Zygmund operators on the space BMO, Rev. Mat. Complut. 20 (2007), no. 2, 523–554.%$

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

Key words: T(1) theorem for BMO, Hörmander condition, Daubechies wavelets, Bony paraproducts, BCR algorithm, pseudo-annular decomposition.
2000 Mathematics Subject Classification: primary 42B20, 42C15; secondary 47A66.