论文标题
加权莫雷空间上凯奇型积分换向器的界限和紧凑性
Boundedness And Compactness Of Cauchy-Type Integral Commutator On Weighted Morrey Spaces
论文作者
论文摘要
In this paper we study the boundedness and compactness characterizations of the commutator of Cauchy type integrals $\mathcal C$ on a bounded strongly pseudoconvex domain $D$ in $C^n$ with boundary $bD$ satisfying the minimum regularity condition $C^{2}$ based on the recent result of Lanzani-Stein and Duong-Lacey-Li-Wick-Wu.我们指出，在此设置中，Cauchy类型的$ \ Mathcal C $是必需部分$ \ Mathcal {C}^\ Sharp $的总和，这是Calderón-Zygmund操作员，其余的$ \ Mathcal R $不再是ACalderón-calderón-Zygmund Operator。我们表明，换向器$ [B，\ Mathcal c] $在加权的Morrey空间上$ l_ {V}^{p，κ}（bd）$（$ v \ in A_p，1 <p <\ infty $），并且仅当$ b $在$ bd $ bmo space上时，只有$ bd $。此外，换向器$ [b，\ mathcal c] $在加权的莫雷空间上是紧凑的$ l_ {v}^{p，κ}（bd）$（$ v \ in a_p，1 <p <\ infty $），并且仅当$ b $在$ bd $上均为$ bd $。
In this paper we study the boundedness and compactness characterizations of the commutator of Cauchy type integrals $\mathcal C$ on a bounded strongly pseudoconvex domain $D$ in $C^n$ with boundary $bD$ satisfying the minimum regularity condition $C^{2}$ based on the recent result of Lanzani-Stein and Duong-Lacey-Li-Wick-Wu. We point out that in this setting the Cauchy type integral $\mathcal C$ is the sum of the essential part $\mathcal{C}^\sharp$ which is a Calderón-Zygmund operator and a remainder $\mathcal R$ which is no longer a Calderón-Zygmund operator. We show that the commutator $[b, \mathcal C]$ is bounded on weighted Morrey space $L_{v}^{p,κ}(bD)$ ($v\in A_p, 1<p<\infty$) if and only if $b$ is in the BMO space on $bD$. Moreover, the commutator $[b, \mathcal C]$ is compact on weighted Morrey space $L_{v}^{p,κ}(bD)$ ($v\in A_p, 1<p<\infty$) if and only if $b$ is in the VMO space on $bD$.
