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Singular integral operators and a $${\overline{\partial }}$$ ∂ ¯ -problem for $$(\varphi ,\psi )$$ ( φ , ψ ) -harmonic functions
Analysis and Mathematical Physics ( IF 1.7 ) Pub Date : 2021-08-20 , DOI: 10.1007/s13324-021-00590-5
José Luis Serrano Ricardo 1 , Ricardo Abreu Blaya 1 , Juan Bory Reyes 2
Affiliation  

This paper aims at proving the boundedness property of multidimensional singular integral operators associated with \((\varphi ,\psi )\)-harmonic functions, which are connected by the use of two orthogonal basis of the Euclidean space \({{\mathbb {R}}}^m\). Besides, necessary and sufficient conditions for the solvability of the \({\overline{\partial }}\)-problem for such \((\varphi ,\psi )\)-harmonic functions are described. The basic devices that make it possible to state and prove both results are borrowed from Clifford analysis.



中文翻译:

奇异积分运算符和 $${\overline{\partial }}$$ ∂ ¯ -$$(\varphi ,\psi )$$ ( φ , ψ ) - 谐波函数的问题

本文旨在证明与\((\varphi ,\psi )\) -调和函数相关的多维奇异积分算子的有界性,它们通过使用欧氏空间的两个正交基\({{\mathbb {R}}}^m\)。此外,描述了此类\((\varphi ,\psi )\) -谐波函数的\({\overline{\partial }}\) - 问题的可解性的充分必要条件。使陈述和证明这两个结果成为可能的基本方法是从 Clifford 分析中借用的。

更新日期:2021-08-20
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