Paraproduct

In mathematics, a paraproduct is a non-commutative bilinear operator acting on functions that in some sense is like the product of the two functions it acts on. According to Svante Janson and Jaak Peetre, in an article from 1988, "the name 'paraproduct' denotes an idea rather than a unique definition; several versions exist and can be used for the same purposes." The concept emerged in J.-M. Bony’s theory
of paradifferential operators,
This said, for a given operator formula_1 to be defined as a paraproduct, it is normally required to satisfy the following properties:
A paraproduct may also be required to satisfy some form of Hölder's inequality.