Mathematical Sciences: Function Theory in Bergman Spaces

在这个项目中，首席研究员将研究 伯格曼空间中涉及函数论的各种问题。 他将特别寻求为伯格曼建立一个理论 空间A**2类似于经典理论， 哈代空间H**2. 他的工作将建立在最近的成果基础上， 在伯格曼的语境中， 空间的作用与边界值的概念相同 在哈代空间中。 函数论中的几个重要问题 涉及到哈代空间的概念。 一个哈代空间是一组 平方可积的全纯函数。 最近 研究人员已经发现了另一类函数， 称为伯格曼空间，具有哈代的许多性质 空间. 在这个项目中，首席研究员将继续 为伯格曼空间发展一个类似于 哈代空间的经典理论。

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.