论文标题
关于双线性最大calderón-zygmund奇异积分运算符的换向器的加权紧凑性
On weighted Compactness of commutators of bilinear maximal Calderón-Zygmund singular integral operators
论文作者
论文摘要
令$ t $为双线性calderón-zygmund单数积分操作员，$ t^*$是其相应的截断最大运算符。对于任何$ b \ in \ text {bmo}（\ mathbb {r}^n）$和$ \ vec {b} =（b_1，\ b_2）\ in \ in \ text {bmo} $ t^*_ {b，j} $（j = 1,2），$ t^*_ {\ vec {b}} \ $分别是j-thenter和$ t^*$的迭代换向器中的换向器。在本文中，对于所有$ 1 <p_1，p_2 <\ infty $，$ \ frac {1} {p} = \ frac {1} {1} {p_1}+\ frac {1} {p_2} {p_2} $ $ l^{p_1}（w_1）\ times l^{p_2}（w_2）$ to $ l^p（v _ {v _ {\ vec {w}}）$，如果$ b，b_1，b_1，b_2 \ in {\ rm cmo}（\ rm cmo}（\ rm cmo}（ $ \ vec {w} =（w_1，w_2）\ in a _ {\ vec {p}} $，$ v _ {\ vec {w}} = w_1^{p/p_1}这里$ {\ rm cmo}（\ mathbb {r}^n）$表示$ \ mathcal {c} _c} _c^\ infty（\ Mathbb {r}^n）$ in $ {\ rm bmo}（\ rm bmo}（\ rm bmo}（\ rm bmo}（\ mathbb）） $ a _ {\ vec {p}} $是多重权重类。
Let $T$ be a bilinear Calderón-Zygmund singular integral operator and $T^*$ be its corresponding truncated maximal operator. For any $b\in\text{BMO}(\mathbb {R}^n)$ and $\vec{b}=(b_1,\ b_2)\in\text{BMO}(\mathbb {R}^n)\times\text {BMO}(\mathbb{R}^n)$, let $T^*_{b,j}$ (j=1,2), $T^*_{\vec{b}}\ $ be the commutators in the j-th entry and the iterated commutators of $T^*$, respectively. In this paper, for all $1<p_1,p_2<\infty$, $\frac{1}{p}=\frac{1}{p_1}+\frac{1}{p_2}$, we show that $T^*_{b,j}$ and $T^*_{\vec{b}}$ are compact operators from $L^{p_1}(w_1)\times L^{p_2}(w_2)$ to $L^p(v_{\vec{w}})$, if $b,b_1,b_2\in{\rm CMO}(\mathbb{R}^n)$ and $\vec{w}=(w_1,w_2)\in A_{\vec{p}}$, $v_{\vec{w}}=w_1^{p/p_1}w_2^{p/p_2}$. Here ${\rm CMO}(\mathbb{R}^n)$ denotes the closure of $\mathcal{C}_c^\infty(\mathbb{R}^n)$ in the ${\rm BMO}(\mathbb{R}^n)$ topology and $A_{\vec{p}}$ is the multiple weights class.
