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On strict inclusions of weighted dirichlet spaces of monogenic functions

Published online by Cambridge University Press:  17 April 2009

K. Gürlebeck  and
H. R. Malonek
K. Gürlebeck
Affiliation:
Bauhaus-Universität Weimar Insitute für Mathematik/Physik, Coudray-Str. 13, D-99423 Weimar, GermanyUniversidade de Aveiro, Departamento de Matemática, Campus Universiário de Santiago, P-3810–193 Aveiro, Portugal
H. R. Malonek
Affiliation:
Bauhaus-Universität Weimar Insitute für Mathematik/Physik, Coudray-Str. 13, D-99423 Weimar, GermanyUniversidade de Aveiro, Departamento de Matemática, Campus Universiário de Santiago, P-3810–193 Aveiro, Portugal
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Abstract

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We consider a scale of weighted spaces a quaternion-valued functions of three real variables. This scale generalises the idea of Qp-spaces in complex function theory. The goal of this paper is to prove that the inclusions of spaces from the scale are strict inclusion. As a tool we prove some properties of special monogenic polynomials which have an importance in their own right independently of their use in the scale of Qp-spaces.

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 64 , Issue 1 , August 2001 , pp. 33 - 50
Copyright
Copyright © Australian Mathematical Society 2001

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