Abstract
The Hardy spaces H2(B) and H2(H+), where B and H+ denote, respectively, the open unit ball of the quaternions and the half space of quaternions with positive real part, as well as Blaschke products, have been intensively studied in a series of papers where they are used as a tool to prove other results in Schur analysis. This paper gives an overview on the topic, collecting the various results available.
Highlights
In this paper we give an overview of the results available on the Hardy spaces H2(Ω) where Ω is either the open unit ball of the quaternions or the half space of quaternions with positive real part
Is either the open unit ball of the quaternions or the half space of quaternions with positive real part. These spaces have been studied in a series of papers, see [1, 2, 3, 4, 5, 6] as a tool to prove other results in Schur analysis and the purpose of this survey is to collect them in one paper
We will work in the framework of slice hyperholomorphic functions
Summary
In this paper we give an overview of the results available on the Hardy spaces H2(Ω) where Ω is either the open unit ball of the quaternions or the half space of quaternions with positive real part. These spaces have been studied in a series of papers, see [1, 2, 3, 4, 5, 6] as a tool to prove other results in Schur analysis and the purpose of this survey is to collect them in one paper. The class of (left) slice hyperholomorphic functions includes, in particular, converging power series with quaternionic coefficients written on the right.
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