On a left-α-ψ-hyperholomorphic Bergman space - González-Cervantes, J. Oscar (Complex variables and elliptic equations, 2023)
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.