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On the harmonic Zygmund spaces. (English) Zbl 1439.30082

Summary: 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.

MSC:

30H30 Bloch spaces
31A05 Harmonic, subharmonic, superharmonic functions in two dimensions
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