论文标题
弱类型端点估计值，用于粗糙单数积分运算符的换向器
Weak Type Endpoint Estimates for the Commutators of Rough Singular Integral Operators
论文作者
论文摘要
令$ω$表示零度均值，并且在单位球体上的平均值为零，$ {s}^{n-1} $，$t_Ω$是卷积单数积分运算符，带有内核$ \ frac {ω（x）} {| x |^n} $。对于$ b \ in {\ rm bmo}（\ mathbb {r}^n）$，让$ t_ {ω，\，\，b} $为$t_Ω$的换向器。在本文中，通过建立合适的稀疏统治，作者建立了$ t_ {ω，\，b} $的$ l \ log l $类型的一些弱类型端点估计值，当$ t_ {ω，\，b} $当$ω\ in l^q（s^{n-1}）$ in L^q（s^{n-1}）$ for某些$ q \ in（1，\，\ iffty] $。
Let $Ω$ be homogeneous of degree zero and have mean value zero on the unit sphere ${S}^{n-1}$, $T_Ω$ be the convolution singular integral operator with kernel $\frac{Ω(x)}{|x|^n}$. For $b\in{\rm BMO}(\mathbb{R}^n)$, let $T_{Ω,\,b}$ be the commutator of $T_Ω$. In this paper, by establishing suitable sparse dominations, the authors establish some weak type endpoint estimates of $L\log L$ type for $T_{Ω,\,b}$ when $Ω\in L^q(S^{n-1})$ for some $q\in (1,\,\infty]$.
