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- W4286387022 abstract "In this paper we consider two weight bump conditions for higher order commutators. Given $b$ and a Calder'on-Zygmund operator $T$, define the commutator $T^1_bf=[T,b]f= bTf-T(bf)$, and for $mgeq 2$ define the iterated commutator $T^m_b f = [b,T_b^{m-1}]f$. Traditionally, commutators are defined for functions $bin BMO$, but we show that if we replace $BMO$ by an oscillation class first introduced by P'erez [31], we can give a range of sufficient conditions on a pair of weights $(u,v)$ for $T^m_b : L^p(v)rightarrow L^p(u)$ to be bounded. Our results generalize work of the first two authors in [10], and more recent work by Lerner, et al. [28]. We also prove necessary conditions for the iterated commutators to be bounded, generalizing results of Isralowitz, et al.[20]." @default.
- W4286387022 created "2022-07-22" @default.
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- W4286387022 date "2021-03-11" @default.
- W4286387022 modified "2023-09-24" @default.
- W4286387022 title "New oscillation classes and two weight bump conditions for commutators" @default.
- W4286387022 doi "https://doi.org/10.48550/arxiv.2103.06821" @default.
- W4286387022 hasPublicationYear "2021" @default.
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