论文标题
Riesz换向器的紧凑性在两个重量设置中转换
Compactness of commutator of Riesz transforms in the two weight setting
论文作者
论文摘要
我们表征了在绽放设置中的换向器的紧凑性。也就是说，对于适当的非脱位calderón-zygmund运算符$ t $，以及一对权重$σ，ω\在a_p $中，换向器$ [t，b] $是从$ l ^{p}（p}（σ）\ to l ^{p} $ b的$ b n时，从$ l ^{p}（p}（σ）） （σ/ω） ^{1/ p} $。这扩展了第一作者福尔摩斯和威克的工作。加权$ VMO $空间与经典的$ VMO $空间不同。在尺寸$ d = 1 $中，紧凑的支持和平滑功能在$ vmo _ {ν} $中密集，但是这不必在尺寸中$ d \ geq 2 $。此外，还研究了产品设置中相对于小VMO空间的换向器。
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\in A_p$, the commutator $ [T, b]$ is compact from $ L ^{p} (σ) \to L ^{p} (ω)$ if and only if $ b \in VMO _{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 $ VMO _{ν}$, but this need not hold in dimensions $ d \geq 2$. Moreover, the commutator in the product setting with respect to little VMO space is also investigated.
