论文标题
在扩展Calderón-Zygmund型奇异积分及其换向器时
On extension of Calderón-Zygmund type singular integrals and their commutators
论文作者
论文摘要
在最近的作品[Huan Yu，Quansen Jiu和Dongsheng Li，2021年]和[Yanping Chen和Zihua Guo，2021年]中，我们研究了Calderón-Zygmund型奇异型单数积分的以下扩展。 \ int _ {\ mathbb {r}^n} \ frac {ω（y）} {| y |^{n-β}} f（x-y）\，$ $ $ $ $ $ $ $ $ 0，$ 0 for $ 0 <β<n $及其交换器。我们在Lipschitz空间，耐寒空间和Muckenhoupt $ a_p $ watered $ l^p $ - 空格上建立了这些奇异积分的估计。我们还建立了其换向器的Lebesgue和Hardy空间估算。我们的估计值在小$β$中是均匀的，因此，可以将限制以$β\至0 $传递，以推断经典的calderón-Zygmund型奇异积分及其换向器的类似估计。
Motivated by the recent works [Huan Yu, Quansen Jiu, and Dongsheng Li, 2021] and [Yanping Chen and Zihua Guo, 2021], we study the following extension of Calderón-Zygmund type singular integrals $$ T_βf (x) = p.v. \int_{\mathbb{R}^n} \frac{Ω(y)}{|y|^{n-β}} f(x-y) \, dy, $$ for $0 < β< n$, and their commutators. We establish estimates of these singular integrals on Lipschitz spaces, Hardy spaces and Muckenhoupt $A_p$-weighted $L^p$-spaces. We also establish Lebesgue and Hardy space estimates of their commutators. Our estimates are uniform in small $β$, and therefore one can pass onto the limits as $β\to 0$ to deduce analogous estimates for the classical Calderón-Zygmund type singular integrals and their commutators.
