Rickart algebras,II |
| |
Authors: | David Handelman |
| |
Institution: | Department of Mathematics, University of Ottawa, Ontario, K1N 6N5, Canada |
| |
Abstract: | The theory of inner-outer factorization in the Hardy spaces Hp in the unit disc is well known and has many applications. It does not carry over to the spaces Hp on the polydisc n or the ball n when n > 1. However, for Lumer's Hardy spaces (LH)p on any simply connected complex analytic manifold, we introduce the notions of internal and external functions and prove that every f? (LH)p has a factorization f = Iε × Eε, where Iε is internal and Eε is external, and Eε? (LH)p?ε, for any ε > 0. The factorization is not unique and an example of Rudin shows that the ε is needed, at least when , where m is an integer. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|