The C-property for slice regular functions and applications to the Bergman space

Abstract

This paper has a twofold purpose: on one hand we deepen the study of slice regular functions by studying their behavior with respect to the so-called C-property and anti-C-property. We show that, for any fixed basis of the algebra of quaternions $\mathbb{H}$ any slice regular function decomposes into the sum of four slice regular components each of them satisfying the C-property. Then, we will use these results to show a reproducing property of the Bergman kernels of the second kind.

Cited by in corpus (4)

• Slice regular Besov spaces of hyperholomorphic functions and composition operators
• On Some Geometric Properties of Slice Regular Functions of a Quaternion Variable
• Bloch, Besov and Dirichlet spaces of slice hyperholomorphic functions
• Quaternionic Fock space in an Euclidean unit ball ${\mathbb{B}}^n$