On Riesz systems of harmonic conjugates in

In continuation of recent studies, we discuss two constructive approaches for the generation of harmonic conjugates to find null solutions to the Riesz system in . This class of solutions coincides with the subclass of monogenic functions with values in the reduced quaternions. Our first algorithm for harmonic conjugates is based on special systems of homogeneous harmonic and monogenic polynomials, whereas the second one is presented by means of an integral representation. Some examples of function spaces illustrating the techniques involved are given. More specifically, we discuss the (monogenic) Hardy and weighted Bergman spaces on the unit ball in consisting of functions with values in the reduced quaternions. We end up proving the boundedness of the underlying harmonic conjugation operators in certain weighted spaces. Copyright © 2013 John Wiley & Sons, Ltd.