Quaternionic Carleson measures
Functional Analysis
2025-12-09 v1 Complex Variables
Abstract
In this paper we provide a general construction of a quaternionic Banach space of slice regular functions from a given Banach space of holomorphic functions, which we call its quaternionic lift. To the best of our knowledge, this construction encompasses all known examples of quaternionic Banach spaces of slice regular functions in the literature. Our main result is a characterization of Carleson and vanishing Carleson measures for such quaternionic Banach function spaces in terms of the corresponding Carleson measures of the underlying holomorphic function space. This offers a unified approach to a problem that so far has been treated on a case-by-case basis.
Cite
@article{arxiv.2512.06831,
title = {Quaternionic Carleson measures},
author = {Nikolaos Chalmoukis and Giulia Sarfatti},
journal= {arXiv preprint arXiv:2512.06831},
year = {2025}
}
Comments
17 pages