Free interpolation for the Zygmund class-Reference-Cited by-同舟云学术

Free interpolation for the Zygmund class

Published:2021-07-01 Issue:6 Volume:28 Page:989-993
ISSN:1072-947X
Container-title:Georgian Mathematical Journal
language:en
Short-container-title:

Author:

Tugores Francesc¹^ORCID,Tugores Laia²^ORCID

Affiliation:

1. Department of Mathematics , University of Vigo , 32004 Ourense , Spain

2. Department of Mathematics , Mary Help of Christians College , 32003 Ourense , Spain

Abstract

Abstract We 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}}

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/gmj-2021-2103/pdf

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