论文标题
Cauchy-szegő$ \ Mathbb c^n $的换向器，其平滑度最低：加权规律性
The commutator of the Cauchy--Szegő Projection for domains in $\mathbb C^n$ with minimal smoothness: weighted regularity
论文作者
论文摘要
令$ d \ subset \ mathbb c^n $为一个有界的，强烈的pseudoconvex域，其边界$ bd $满足了$ c^2 $的最小规律性条件，让$s_Ω$表示Cauchy--szegő投影，对（任何）持续多$ fosecuse doffication doffication n of（a）我们表征了Lebesgue Space $ l^p（bd，ω_p）$的换向器$ [b，s_Ω] $的紧凑性和界限（后者具有明确的边界），其中$ω_p$是muckenhoupt类$ a_p（bd）$，$ 1 <p <p <p <p <p <\ fefty $中的$ω_p$。下一个修复$ p = 2 $，我们让$ s_ {ω_2} $表示cauchy-szegő投影在A_2（bd）$中定义的$ω_2\定义的投影，这是可以定义Cauchy-Leray措施的有意义的参考度量的最大参考度量。我们表征了换向器$ \ displayStyle {[b，s_ {ω_2}]} $的$ l^2（bd，ω_2）$中的有界性和紧凑性。
Let $D\subset\mathbb C^n$ be a bounded, strongly pseudoconvex domain whose boundary $bD$ satisfies the minimal regularity condition of class $C^2$, and let $S_ω$ denote the Cauchy--Szegő projection defined with respect to (any) positive continuous multiple $ω$ of induced Lebesgue measure for the boundary of $D$. We characterize compactness and boundedness (the latter with explicit bounds) of the commutator $[b, S_ω]$ in the Lebesgue space $L^p(bD, Ω_p)$ where $Ω_p$ is any measure in the Muckenhoupt class $A_p(bD)$, $1<p<\infty$. We next fix $p =2$ and we let $S_{Ω_2}$ denote the Cauchy--Szegő projection defined with respect to (any) measure $Ω_2 \in A_2(bD)$, which is the largest class of reference measures for which a meaningful notion of Cauchy-Leray measure may be defined. We characterize boundedness and compactness in $L^2(bD, Ω_2)$ of the commutator $\displaystyle{[b,S_{Ω_2}]}$.
