论文标题
Schatten类Bergman-type和Szegö-type操作员在有限的对称域上
Schatten class Bergman-type and Szegö-type operators on bounded symmetric domains
论文作者
论文摘要
这是我们在伯格曼型操作员上对有限域进行的第三项工作。在前两篇文章中，我们系统地研究了伯格曼型在希尔伯特单位球上的界限，紧凑性和夏情化的成员身份。在本文中，我们研究了由伯格曼内核和SzegöKernel引起的单数积分运算符，以其标准的Harish-Chandra实现中的不可约定有限的对称域。我们完全表征了伯格曼型运算符和szegö-type操作员属于有界对称域的几个分析数值不变性的属于沙滕类运算符的理想。这些结果概括了由于作者及其合着者而概括了希尔伯特单位球的最新结果，但也涵盖了所有不可还原有限的对称域。此外，我们获得了两个痕量公式和一个与前纹鲁丁估计有关的新的积分估计。证明的关键要素涉及有关界面对称域以及伯格曼型和szegö-type运算符的频谱估计的功能理论。
This is our third work on Bergman-type operator over bounded domains. In the previous two articles, we systematically study the boundedness, compactness and Schatten membership of Bergman-type on the Hilbert unit ball. In the present paper, we investigate singular integral operators induced by the Bergman kernel and Szegö kernel on the irreducible bounded symmetric domain in its standard Harish-Chandra realization. We completely characterize when Bergman-type operators and Szegö-type operators belong to Schatten class operator ideals by several analytic numerical invariants of the bounded symmetric domain. These results generalize a recent result on the Hilbert unit ball due to the author and his coauthor but also cover all irreducible bounded symmetric domains. Moreover, we obtain two trace formulae and a new integral estimate related to the Forelli-Rudin estimate. The key ingredient of the proofs involves the function theory on the bounded symmetric domain and the spectrum estimate of Bergman-type and and Szegö-type operators.
