Mathematical Sciences: Function Theory in Bergman Spaces

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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.