Moscow Mathematical Journal

Volume 14, Issue 3, July–September 2014 pp. 473–489.

Some Integral Representations of Slice Hyperholomorphic Functions

Authors: F. Colombo (1), J. O. González-Cervantes (2), and I. Sabadini (1)
Author institution:(1) Politecnico di Milano, Dipartimento di Matematica, Via E. Bonardi, 9, 20133 Milano, Italy
(2) Departamento de Matemáticas, E.S.F.M. del I.P.N. 07338, México D.F., México

Summary:

In this paper we prove the analog of the Schwarz integral formula as well as other integral representations for slice monogenic functions. The key tool to establish these formulas is a suitable decomposition of slice monogenic functions. All the results that are stated in the case of slice monogenic functions hold also for slice regular functions of a quaternionic variable.

2010 Mathematics Subject Classification. 30G35.

Keywords: Slice monogenic functions, Schwarz integral formula, Harnack inequalities.

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