论文标题
关于伯格曼型整体操作员的紧凑性
On the compactness of Bergman-type integral operators
论文作者
论文摘要
伯格曼型整体运营商是复杂分析和操作者理论的经典运营商。最近，第一作者及其合作者\ cite {diw}完全表征了$ l^p $ - $ l^q $ bergman-type积分运算符$k_α，k_α^+$和$ l^p $ - $ l^p $ -l^q $ $k_α$ $k_α$的$k_α^+$。在本文中，我们将使用一种实质性的新方法来完全表征$k_α^+，$的$ l^p $ - $ l^q $ compactness，但也证明了$ l^p $ - $ l^q $ co $k_α^+$实际上相当于。此外，我们完全表征了Schatten类和Macaev类Bergman-Type积分操作员$k_α$，$ l^2 $空间和伯格曼空间，通过与单位球的尺寸相关的不平等现象，我们还通过引入综合运营商Hausdorff尺寸的概念来提供内在的特征。本文还计算出$k_α$的二毫克痕迹。
Bergman-type integral operators are classical operators in complex analysis and operator theory. Recently, the first author and his collaborator \cite{DiW} completely characterized the $L^p$-$L^q$ boundedness of Bergman-type integral operators $K_α,K_α^+$ and the $L^p$-$L^q$ compactness of $K_α$ on the unit ball. In this paper, we will use a substantially new method to completely characterize the $L^p$-$L^q$ compactness of $K_α^+,$ but also prove that the $L^p$-$L^q$ compactness of operators $K_α,K_α^+$ is in fact equivalent. Moreover, we completely characterize Schatten class and Macaev class Bergman-type integral operator $K_α$ on $L^2$ space and Bergman space via inequalities related to the dimension of the unit ball, and we also give an intrinsic characterization by introducing the concept of Hausdorff dimension of compact operators. The Dixmier trace of $K_α$ are also calculated in this paper.
