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ON THE HARMONIC ZYGMUND SPACES

Published online by Cambridge University Press:  11 March 2020

MUNIRAH ALJUAID
Affiliation:
Department of Mathematics, Northern Borders University, Arar 73222, Saudi Arabia email maljuaid@gmu.edu
FLAVIA COLONNA*
Affiliation:
Department of Mathematical Sciences, George Mason University, Fairfax, VA 22030, USA email fcolonna@gmu.edu

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.

Type
Research Article
Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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