# Free interpolation for the Zygmund class

Free interpolation for the Zygmund class AbstractWe introduce interpolation sets for the Zygmund class 𝒵{\mathcal{Z}}in the unit disc of the complex plane. This space lies between the Lipschitz classes of order α, 0<α<1{0<\alpha<1}, and the class of order α=1{\alpha=1}, whose interpolation sets are given in a different way.We prove that the interpolation sets for 𝒵{\mathcal{Z}}are interpolation sets for the Lipschitz classes of order α, 0<α<1{0<\alpha<1}, and the latter are interpolation sets for a space slightly larger than 𝒵{\mathcal{Z}}. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Georgian Mathematical Journal de Gruyter

# Free interpolation for the Zygmund class

, Volume 28 (6): 5 – Dec 1, 2021
5 pages

/lp/de-gruyter/free-interpolation-for-the-zygmund-class-jggXj8n20B
Publisher
de Gruyter
© 2021 Walter de Gruyter GmbH, Berlin/Boston
ISSN
1572-9176
eISSN
1572-9176
DOI
10.1515/gmj-2021-2103
Publisher site
See Article on Publisher Site

### Abstract

AbstractWe introduce interpolation sets for the Zygmund class 𝒵{\mathcal{Z}}in the unit disc of the complex plane. This space lies between the Lipschitz classes of order α, 0<α<1{0<\alpha<1}, and the class of order α=1{\alpha=1}, whose interpolation sets are given in a different way.We prove that the interpolation sets for 𝒵{\mathcal{Z}}are interpolation sets for the Lipschitz classes of order α, 0<α<1{0<\alpha<1}, and the latter are interpolation sets for a space slightly larger than 𝒵{\mathcal{Z}}.

### Journal

Georgian Mathematical Journalde Gruyter

Published: Dec 1, 2021

Keywords: Interpolation set; Zygmund class; Lipschitz classes; separation conditions; 30E05; 30H50; 30J10