Polyanalytic Hardy decomposition of higher order Lipschitz functions

This paper is concerned with the problem of decomposing a higher order Lipschitz function on a closed Jordan curve Γ into a sum of two polyanalytic functions in each open domain defined by Γ. Our basic tools are the Hardy projections related to a singular integral operator arising in polyanalytic fu...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2021-01, Vol.493 (2), p.124559, Article 124559
Main Authors: Abreu Blaya, Ricardo, De la Cruz Toranzo, Lianet
Format: Article
Language:English
Subjects:
Hardy projections
Higher order Lipschitz classes
Polyanalytic functions
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Summary:This paper is concerned with the problem of decomposing a higher order Lipschitz function on a closed Jordan curve Γ into a sum of two polyanalytic functions in each open domain defined by Γ. Our basic tools are the Hardy projections related to a singular integral operator arising in polyanalytic function theory, which, as it is proved here, represents an involution operator on the higher order Lipschitz classes. Our result generalizes the classical Hardy decomposition of Hölder continuous functions on the boundary of a domain.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2020.124559