Mathematical Sciences: Function Theory in Bergman Spaces

在这个项目中，首席研究员将研究Bergman空间中涉及函数论的各种问题。特别是，他将寻求为Bergman空间A**2建立一个类似于Hardy空间H**2的经典理论的理论。他的工作将建立在基于“支配”概念的最新结果的基础上，在Bergman空间的背景下，它起着与Hardy空间背景下的边值概念相同的作用。函数论中的各种重要问题都涉及到Hardy空间的概念。Hardy空间是一组平方可积的全纯函数。最近，研究人员发现，一类不同的函数，称为Bergman空间，具有Hardy空间的许多性质。在这个项目中，首席研究员将继续发展一种类似于经典Hardy空间理论的Bergman空间理论。

In this project the principal investigator will examine various questions involving function theory in Bergman spaces. In particular, he will seek to establish a theory for the Bergman space A**2 that is analogous to the classical theory for the Hardy space H**2. His work will build upon recent results based on the concept of "domination", which in the context of Bergman spaces plays the same role as does the concept of boundary values in the context of Hardy spaces. Various important problems in the theory of functions involve the notion of a Hardy space. A Hardy space is a set of holomorphic functions whose squares are integrable. Recently researchers have discovered that a different class of functions, called a Bergman space, shares many of the properties of Hardy spaces. In this project the principal investigator will continue to develop a theory for Bergman spaces that is analogous to the classical theory of Hardy spaces.