Iterated paraproducts and iterated commutator estimates in Besov spaces

Abstract

In the previous study [6], the author provided an algebraic proof of the multicomponent commutator estimate in Besov spaces $C^{\alpha}=B_{\infty,\infty}^{\alpha}$ with $0 < \alpha < 1$. In this paper, we extend that result to general Besov spaces $B_{p,q}^{\alpha}$ with $p, q \in [1,\infty]$ and $0 < \alpha < 1$.