Hilbert transforms and the Cauchy integral
in euclidean space
Studia Mathematica, Tome 193 (2009) no. 2, pp. 161-187
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
Keywords:
generalize notions harmonic conjugate functions hilbert transforms higher dimensional euclidean spaces setting differential forms hodge dirac system these harmonic conjugates general far being unique under suitable boundary conditions prove existence uniqueness conjugates proof yields invertibility results class generalized double layer potential operators lipschitz surfaces boundedness related hilbert transforms
Affiliations des auteurs :
Andreas Axelsson 1 ; Kit Ian Kou 2 ; Tao Qian 2
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author = {Andreas Axelsson and Kit Ian Kou and Tao Qian},
title = {Hilbert transforms and the {Cauchy} integral
in euclidean space},
journal = {Studia Mathematica},
pages = {161--187},
publisher = {mathdoc},
volume = {193},
number = {2},
year = {2009},
doi = {10.4064/sm193-2-4},
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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 SP - 161 EP - 187 VL - 193 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/sm193-2-4/ DO - 10.4064/sm193-2-4 LA - en ID - 10_4064_sm193_2_4 ER -
%0 Journal Article %A Andreas Axelsson %A Kit Ian Kou %A Tao Qian %T Hilbert transforms and the Cauchy integral in euclidean space %J Studia Mathematica %D 2009 %P 161-187 %V 193 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/sm193-2-4/ %R 10.4064/sm193-2-4 %G en %F 10_4064_sm193_2_4
Andreas Axelsson; Kit Ian Kou; Tao Qian. Hilbert transforms and the Cauchy integral in euclidean space. Studia Mathematica, Tome 193 (2009) no. 2, pp. 161-187. doi: 10.4064/sm193-2-4
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