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ON THE HARMONIC ZYGMUND SPACES

Part of: Two-dimensional theory Spaces and algebras of analytic functions

Published online by Cambridge University Press:  11 March 2020

MUNIRAH ALJUAID Open the ORCID record for MUNIRAH ALJUAID [Opens in a new window]  and
FLAVIA COLONNA Open the ORCID record for FLAVIA COLONNA [Opens in a new window]
MUNIRAH ALJUAID
Affiliation:
Department of Mathematics, Northern Borders University, Arar 73222, Saudi Arabia email [email protected]
FLAVIA COLONNA*
Affiliation:
Department of Mathematical Sciences, George Mason University, Fairfax, VA 22030, USA email [email protected]
*
✉[email protected]
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Abstract

In this paper we study a class ${\mathcal{Z}}_{H}$ of harmonic mappings on the open unit disk $\mathbb{D}$ in the complex plane that is an extension of the classical (analytic) Zygmund space. We extend to the elements of this class a characterisation that is valid in the analytic case. We also provide a similar result for a closed separable subspace of ${\mathcal{Z}}_{H}$ which we call the little harmonic Zygmund space.

Keywords

harmonic mappingBloch spaceZygmund spacegrowth space

MSC classification

Primary: 30H30: Bloch spaces
Secondary: 31A05: Harmonic, subharmonic, superharmonic functions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 101 , Issue 3 , June 2020 , pp. 466 - 476
Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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