A Global Wavefront Set Condition for Defining Bony's Paraproduct Decomposition

We establish a natural generalization of the Hörmander condition for the multiplication of Besov distributions using the global wavefront set framework of Coriasco, Johansson, and Toft. Using this condition, we relate the microlocal perspective on multiplication of distributions to the classical paraproduct decomposition of pointwise multiplication arising in the paradifferential calculus of Bony.