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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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
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Abstract 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.
AbstractList 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 isThe 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.
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.
Author González-Cervantes, J. Oscar
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Snippet 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...
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SubjectTerms conformally covariant property
Operators (mathematics)
quaternionic reproducing kernel
Quaternionic weighted Bergman spaces
α-hyperholomorphy function theory
Title On a left-α-ψ-hyperholomorphic Bergman space
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