# Quaternionic Hardy spaces

created by stoppato on 09 Nov 2016
modified by sarfatti on 19 Feb 2020

[BibTeX]

Published Paper

Inserted: 9 nov 2016
Last Updated: 19 feb 2020

Journal: Ann. Sc. Norm. Super. Pisa Cl. Sci. (5)
Year: 2018
Doi: 10.2422/2036-2145.201502_008

ArXiv: 1404.1234 PDF
The theory of slice regular functions of a quaternionic variable, introduced in 2006 by Gentili and Struppa, extends the notion of holomorphic function to the quaternionic setting. This fast growing theory is already rich of many results and has interesting applications. In this setting, the present paper is devoted to introduce and study the quaternionic counterparts of Hardy spaces of holomorphic functions of one complex variable. The basic properties of the theory of quaternionic Hardy spaces are investigated, and in particular a Poisson-type representation formula, the notions of outer function, singular function and inner function are given. A quaternionic (partial) counterpart of the classical $H^p$-factorization theorem is proved. This last result assumes a particularly interesting formulation for a large subclass of slice regular functions, where it is obtained in terms of an outer function, a singular function and a quaternionic Blaschke product.