标题： 关于在$C^n$中的管形及相关区域中的 Bergman 投影和精确分解定理 显示英文标题

标题： On Bergman projections and sharp decomposition theorems in tubular and related domains in $C^n$

摘要： 解析函数空间理论在对称锥上的非常一般的管状域是一个相对较新的有趣研究领域。 管状域是非常一般且非常复杂的域。 最近，B. Sehba及其合作者在关于此类复杂无界域中的Bergman型算子的论文中提供了该研究领域的几个新结果。 在本文中，我们将他们的结果扩展到管状域乘积中的某些解析函数空间。 我们定义了新的Bergman型积分算子和新的解析混合范数空间在这些类型的域以及管状域的乘积中，并提供了某些Bergman型算子有界性的新结果。 我们的结果在这个研究领域可能有各种良好的应用。 我们的结果通过非常相似的证明可能在第二类Siegel域、有界对称域和具有光滑边界的有界强伪凸域、各种矩阵域中有效。 我们在本文末尾添加了一个Bergman空间的新锐分解定理。 之前，作者在其他域中提供了这种类型的锐分解定理。 我们在Bergman型函数空间中的锐结果扩大了之前已知的多变量解析函数空间中此类断言的列表。 最后，我们还提出了与该研究领域相关的各种有趣的新问题，并且也指出了这些问题的一些具体解决方案方案。 我们在本文的第二部分提供了许多有趣的简短评论和备注。 显示英文摘要

摘要： The theory of analytic function spaces in very general tubular domains over symmetric cones is a relatively new interesting research area. Tube domains are very general and very complicated domains. Recently several new results in this research area were provided in papers of B. Sehba and his coauthors concerning Bergman type operators in such type complicated unbounded domains. In this note we expand their results to certain spaces of analytic functions in products of tube domains. We define new integral operators of Bergman type and new analytic mixed norm spaces in such type domains and products of tube domains and provide new results on boundedness of certain Bergman type operators. Our results may have various nice applications in this research area. Our results with very similar proofs may be valid in Siegel domains of second type, in bounded symmetric domains and bounded strongly pseudoconvex domains with the smooth boundary, various matrix domains. We will add at the end of this note a new sharp decomposition theorem for Bergman space. Previously such type sharp decomposition theorems in analytic function spaces were provided by author in other domains. Our sharp result in Bergman type function spaces enlarge that list of previously known such type assertions in analytic function spaces of several variables. We finnaly pose in addition various interesting new problems related to this research area and moreover indicate also some concrete schemes for solutions of these problems. We also provide in the second part of this note many interesting short comments and remarks.