Weighted estimates for rough singular integrals with applications to angular integrability, II
Weighted estimates for rough singular integrals with applications to angular integrability, II
复制标题
粗奇异积分的加权估计及其在角可积性中的应用，II
DOI：
10.7153/mia-2020-23-31
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发表时间：
2020
影响因子：
1
通讯作者：
伍火熊
中科院分区：
文献类型：
--
作者：
刘风;刘荣辉;伍火熊
本文主要研究一类奇异积分。具有粗糙径向核$h$和球核的算子。$\Omega$以及相应的沿多项式曲线的极大算子。作者通过。建立了这类算子的几个加权估计。假设核$h\equiv1$和$\Omega\in\mathcal{F}_\beta({\rm S}^{n-1})$。或者$h\in\Delta_\gamma(\mathbb{R}_{+})$和。$\Omega\in W\mathcal{F}_\beta({\rm S}^{n-1})$。给你。$\mathcal{F}_\beta({\rm S}^{n-1})$为Grafakos-Stefanov。内核，$W\mathcal{F}_\beta({\rm S}^{n-1})$表示变体。Grafakos-Stefanov内核。作为应用程序，。这类算子在混合径向-角空间上的有界性。获取$L_{|x|}^pL_{\theta}^{q}(\mathbb{R}^n)$。同时给出了相应的向量值版本。此外，在算子的定义中，边界与多项式的系数无关。
This paper is devoted to studying certain singular integral.operators with rough radial kernel $h$ and sphere kernel.$\Omega$ as well as the corresponding maximal operators along polynomial curves. The authors.establish several weighted estimates for such operators by.assuming that the kernels $h\equiv1$ and $\Omega\in\mathcal{F}_\beta({\rm S}^{n-1})$,.or $h\in\Delta_\gamma(\mathbb{R}_{+})$ and.$\Omega\in W\mathcal{F}_\beta({\rm S}^{n-1})$. Here.$\mathcal{F}_\beta({\rm S}^{n-1})$ denotes the Grafakos-Stefanov.kernel and $W\mathcal{F}_\beta({\rm S}^{n-1})$ denotes the variant.of Grafakos-Stefanov kernel. As applications, the.boundedness of such operators on the mixed radial-angular spaces.$L_{|x|}^pL_{\theta}^{q}(\mathbb{R}^n)$ are obtained. Meanwhile, the corresponding vector-valued versions are also given..Moreover, the bounds are independent of the coefficients of the polynomials in the definition of operators.