Polyanalytic Hardy decomposition of higher order Lipschitz functions |
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Authors: | Ricardo Abreu Blaya Lianet De la Cruz Toranzo |
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Institution: | 1. Facultad de Matemáticas, Universidad Autónoma de Guerrero, Mexico;2. Facultad de Informática y Matemática, Universidad de Holguín, Cuba |
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Abstract: | 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. |
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Keywords: | Polyanalytic functions Higher order Lipschitz classes Hardy projections |
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