This paper is concerned with the problem of decomposing a higher order Lipschitz function on a closed Jordan curve $\Gamma$ into a sum of two polyanalytic functions in each open domain defined by $\Gamma$. 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 Holder continuous functions on the boundary of a domain.

中文翻译：

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高阶 Lipschitz 函数的多分析 Hardy 分解

本文关注的是将闭合Jordan曲线$\Gamma$上的高阶​​Lipschitz函数分解为$\Gamma$定义的每个开放域中的两个多解析函数之和的问题。我们的基本工具是与多解析函数理论中出现的奇异积分算子相关的哈代投影，正如这里所证明的那样，它代表了高阶 Lipschitz 类上的对合算子。我们的结果概括了域边界上 Holder 连续函数的经典 Hardy 分解。