A Bloch Constant for Hyperholomorphic Functions¹

Dominic Rochon

June, 2000

Résumé

We use a commutative generalization of complex numbers called bicomplex numbers to show that the subclass of holomorphic mappings of $\mathbb {C}^{2}$ satisfying the complexified Cauchy-Riemann equations has a Bloch constant in $\mathbb {C}^{2}$. Moreover, we find estimates when the mappings are on the unit ball and we give a specific domain of $\mathbb {C}^{2}$ where the Bloch constant has the same value as the classical Bloch constant for one variable.

Keywords: Bicomplex numbers, Bloch constant, Quasiregular mappings.
AMS subject classification: 30G, 30G35, 32A, 32A30.