论文标题
伯格曼投影仪在同质西格尔域上的界限
Boundedness of Bergman projectors on homogeneous Siegel domains
论文作者
论文摘要
在本文中，我们研究了伯格曼投影仪对II型均匀的Siegel域上加权伯格曼空间的界限。由于它在不可还原的对称锥体的特殊情况下似乎是一种自然方法，因此我们研究了混合加权lebesgue空间的规模上的这种界限。 这种操作员的界限的尖锐范围仅在洛伦兹锥体上的管域域中才知道。 在本文中，我们证明了这种伯格曼投影仪的界限等效于原子分解，二元性和混合体加权伯格曼空间边界值的特征的概念，扩展了仅在不可降低的对称锥体上的管域而已才知道的结果。即使在后一个更简单的情况下，我们的一些结果也是新的。 我们还研究了“正”伯格曼投影仪（Bergman Projectors）的简单但仍然很有趣的情况，这是伯格曼内核被其绝对价值取代的整体操作员。我们提供了一个有用的表征，该表征以前是管域的知名度。
In this paper we study the boundedness of Bergman projectors on weighted Bergman spaces on homogeneous Siegel domains of Type II. As it appeared to be a natural approach in the special case of tube domains over irreducible symmetric cones, we study such boundedness on the scale of mixed-norm weighted Lebesgue spaces. The sharp range for the boundedness of such operators is essentially known only in the case of tube domains over Lorentz cones. In this paper we prove that the boundedness of such Bergman projectors is equivalent to variuos notions of atomic decomposition, duality, and characterization of boundary values of the mixed-norm weighted Bergman spaces, extending results moslty known only in the case of tube domains over irreducible symmetric cones. Some of our results are new even in the latter simpler context. We also study the simpler, but still quite interesting, case of the "positive" Bergman projectors, the integral operator in which the Bergman kernel is replaced by its absolute value. We provide a useful characterization which was previously known for tube domains.
