Journal of Operator Theory

Volume 79, Issue 1, Winter 2018 pp. 33-54.

Two weight inequalities for iterated commutators with Calderon-Zygmund operators

Authors: Irina Holmes (1) and Brett D. Wick (2)
Author institution: (1) Department of Mathematics, Michigan State University, East Lansing, 48824, U.S.A.
(2) Department of Mathematics, Washington University in St. Louis, St. Louis, 6310, U.S.A.

Summary: Given a Calderon-Zygmund operator $T$, a classic result of Coifman, Rochberg and 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 $\| [b, T] : L^p(\mathbb{R}^n;\mu) \to L^p(\mathbb{R}^n;\lambda)\|$ 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 and Perez in the process.

DOI: http://dx.doi.org/10.7900/jot.2016feb24.2160
Keywords: commutators, Calderon-Zygmund operators, bounded mean oscillation, weights

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