Hilbert transforms and the Cauchy integral in euclidean space

Andreas Axelsson, Kit Ian Kou, and Tao Qian. "Hilbert transforms and the Cauchy integral in euclidean space." Studia Mathematica 193.2 (2009): 161-187. <http://eudml.org/doc/284669>.

@article{AndreasAxelsson2009,
abstract = {We generalize the notions of harmonic conjugate functions and Hilbert transforms to higher-dimensional euclidean spaces, in the setting of differential forms and the Hodge-Dirac system. These harmonic conjugates 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.},
author = {Andreas Axelsson, Kit Ian Kou, Tao Qian},
journal = {Studia Mathematica},
keywords = {Cauchy integral; Dirac equation; double layer potential; Hilbert transform; harmonic conjugates; Lipschitz domain; invertibility},
language = {eng},
number = {2},
pages = {161-187},
title = {Hilbert transforms and the Cauchy integral in euclidean space},
url = {http://eudml.org/doc/284669},
volume = {193},
year = {2009},
}

TY - JOUR
AU - Andreas Axelsson
AU - Kit Ian Kou
AU - Tao Qian
TI - Hilbert transforms and the Cauchy integral in euclidean space
JO - Studia Mathematica
PY - 2009
VL - 193
IS - 2
SP - 161
EP - 187
AB - We generalize the notions of harmonic conjugate functions and Hilbert transforms to higher-dimensional euclidean spaces, in the setting of differential forms and the Hodge-Dirac system. These harmonic conjugates 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.
LA - eng
KW - Cauchy integral; Dirac equation; double layer potential; Hilbert transform; harmonic conjugates; Lipschitz domain; invertibility
UR - http://eudml.org/doc/284669
ER -