A renormalization algorithm for pointwise products

The "correction algorithm", applied in probability theory to the product of two martingales, has a natural analogue in the real-variable setting. It t urns out that the corresponding bilinear operators obtained in this way pro vide us with a new "renormalization algorithm", in the sense of Coifman-Dob yinsky-Meyer. As a consequence, we obtain a straightforward proof of a clas sical property of the Hilbert transform. (C) 1999 Academie des Sciences / E ditions scientifiques et medicales Elsevier SAS.