Renormalisation du produit, Jacobiens et transformations de Riesz

The “correction algorithm”, applied in probability theory to the pointwise product of two martingales, has a natural analogue in the real-variable setting. It turns out that the corresponding bilinear operators obtained in this way provide us with a new “renormalization algorithm”, in the sense of Coifman, Dobyinski and Meyer. We give a few examples of applications, regarding multidimensional Hardy spaces and various nonlinear quantities.