Year: 2025
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Chalmoukis, Nikolaos, Sarfatti, Giulia
Institutions: Marche Polytechnic University, University of Milano-Bicocca
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G2971504390, G5245466801, G8097609347
OpenAlex ID: W7111240540
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