Compactness of commutator of Riesz transforms in the two weight setting
Compactness of commutator of Riesz transforms in the two weight setting
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DOI：
10.1016/j.jmaa.2021.125869
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发表时间：
2020-10
影响因子：
1.3
通讯作者：
M. Lacey;Ji Li
中科院分区：
文献类型：
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作者：
M. Lacey;Ji Li
我们刻画了Bloom环境中交换子的紧性。也就是说，对于适当的非退化Calderón-Zygmund算子T和一对权σ，ω∈Ap，交换子[T，b]是由L p(σ)→L p(ω))紧的当且仅当b∈V M Oν，其中ν=(σ/ω)1/p.这推广了第一作者Holmes和Wick的工作.加权VMO空间不同于经典的VMO空间。在维d=1时，紧支集和光滑函数在V M Oν中是稠密的，但这在维d≥2时不一定成立.此外，还研究了乘积环境中关于小VMO空间的交换子.
We characterize the compactness of commutators in the Bloom setting. Namely, for a suitably non-degenerate Calderón–Zygmund operator T, and a pair of weights σ, ω∈ A p, the commutator [T, b] is compact from L p (σ)→ L p (ω) if and only if b∈ V M O ν, where ν=(σ/ω) 1/p. This extends the work of the first author, Holmes and Wick. The weighted VMO spaces are different from the classical VMO space. In dimension d= 1, compactly supported and smooth functions are dense in V M O ν, but this need not hold in dimensions d≥ 2. Moreover, the commutator in the product setting with respect to little VMO space is also investigated.