Hilbert transforms and the Cauchy integral in euclidean space
Analysis of PDEs
2009-05-01 v3 Complex Variables
Abstract
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.
Cite
@article{arxiv.0809.4128,
title = {Hilbert transforms and the Cauchy integral in euclidean space},
author = {Andreas Axelsson and Kit Ian Kou and Tao Qian},
journal= {arXiv preprint arXiv:0809.4128},
year = {2009}
}
Comments
Some minor corrections made