In this talk we will revisit an idea of Uchiyama about factorization in Hardy spaces and show how this idea can be implemented in other function spaces. As a result we will obtain factorization theorems for Hardy spaces in multi-parameter settings, multilinear settings, and in the setting of the Bessel operator. Equivalently, we will obtain results about the boundedness of commutators in these settings.
This talk is based on joint work with Ji Li, Xuan Duong, and Donyong Yang.