Two Weight Inequalities for Iterated Commutators with Calderón-Zygmund Operators Academic Article uri icon

abstract

  • Given a Calder'on-Zygmund operator $T$, a classic result of Coifman-Rochberg-Weiss relates the norm of the commutator $[b, T]$ with the BMO norm of $b$. We focus on a weighted version of this result, obtained by Bloom and later generalized by Lacey and the authors, which relates $| [b, T] : L^p(mathbb{R}^n; mu) o L^p(mathbb{R}^n; lambda) |$ to the norm of $b$ in a certain weighted BMO space determined by $A_p$ weights $mu$ and $lambda$. We extend this result to higher iterates of the commutator and recover a one-weight result of Chung-Pereyra-Perez in the process.

author list (cited authors)

  • Holmes, I., & Wick, B. D.

publication date

  • January 1, 2015 11:11 AM