On pointwise and weighted estimates for commutators of Calder\'on-Zygmund operators

Andrei K. Lerner; Sheldy Ombrosi; Israel P. Rivera-Ríos

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arXiv · 1604.01334

On pointwise and weighted estimates for commutators of Calder\'on-Zygmund operators

Andrei K. Lerner·Sheldy Ombrosi·Israel P. Rivera-Ríos

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Abstract

In recent years, it has been well understood that a Calder\'on-Zygmund operator $T$ is pointwise controlled by a finite number of dyadic operators of a very simple structure (called the sparse operators). We obtain a similar pointwise estimate for the commutator $[b,T]$ with a locally integrable function $b$. This result is applied into two directions. If $b\in BMO$, we improve several weighted weak type bounds for $[b,T]$. If $b$ belongs to the weighted $BMO$, we obtain a quantitative form of the two-weighted bound for $[b,T]$ due to Bloom-Holmes-Lacey-Wick.

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BibTeX RIS

Andrei K. Lerner, Sheldy Ombrosi, Israel P. Rivera-Ríos. 2016-04-05. On pointwise and weighted estimates for commutators of Calder\'on-Zygmund operators. https://arxiv.org/abs/1604.01334

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