On a left-α-ψ-hyperholomorphic Bergman space

Given a structural set , some papers [M. Shapiro, V. Vasilevski, (Complex Var Theory Appl. 1995;27:17-46 and 1995;27:67-96)] study the quaternionic ψ-Fueter operator calculus, where the Fueter-type operator is The aim of this paper is to present the function theory and the Bergman theory induced by...

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Bibliographic Details
Published in:	Complex variables and elliptic equations Vol. 68; no. 2; pp. 222 - 236
Main Author:	González-Cervantes, J. Oscar
Format:	Journal Article
Language:	English
Published:	Colchester Taylor & Francis 01.02.2023 Taylor & Francis Ltd
Subjects:	conformally covariant property Operators (mathematics) quaternionic reproducing kernel Quaternionic weighted Bergman spaces α-hyperholomorphy function theory
ISSN:	1747-6933, 1747-6941
Online Access:	Get full text
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Summary:	Given a structural set , some papers [M. Shapiro, V. Vasilevski, (Complex Var Theory Appl. 1995;27:17-46 and 1995;27:67-96)] study the quaternionic ψ-Fueter operator calculus, where the Fueter-type operator is The aim of this paper is to present the function theory and the Bergman theory induced by the ψ-Fueter-type operator: where a is a quaternionic constant and f is a continuously differentiable function. Particularly, this work shows the Stokes and Borel-Pompieu formulas associated to and presents several results of the Bergman theory such as the existence of the Bergman kernel, Bergman projection and their conformal covariant properties.
Bibliography:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	1747-6933 1747-6941
DOI:	10.1080/17476933.2021.1986033