Hilbert transforms and the Cauchy integral in euclidean space

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We generalize the notion of harmonic conjugate functions and Hilbert transforms to higher dimensional euclidean spaces, in the setting of differential forms and the Hodge-Dirac system. These conjugate functions are in general far from being unique, but under suitable boundary conditions we prove existence and uniqueness of conjugates. The proof also yields invertibility results for a new class of generalized double layer potential operators on Lipschitz surfaces and boundedness of related Hilbert transforms.
Some minor corrections made

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Analysis of PDEs, Complex Variables, 45E05; 31B10

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http://salesiana.dossiersoluciones.com/handle/123456789/228824

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0809.4128
 http://arxiv.org/abs/0809.4128

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arXiv