From Hankel operators to Carleson measures in a quaternionic variable

TL;DR

This paper extends classical operator theory results to quaternionic Hardy spaces, introducing Hankel operators and establishing analogues of key theorems like Nehari's and Fefferman's.

Contribution

It develops a theory of Hankel operators in quaternionic analysis and proves foundational theorems similar to classical complex cases.

Findings

Hankel operators are well-defined on quaternionic Hardy spaces

Analogues of Nehari's theorem are established in the quaternionic setting

Connections between Hankel operators and Carleson measures are explored

Abstract

We introduce and study Hankel operators defined on the Hardy space of regular functions of a quaternionic variable. Theorems analogous to those of Nehari anc C. Fefferman are proved.