Hilbert transforms and the Cauchy integral in euclidean space

• Autorzy: Andreas Axelsson , Kit Ian Kou , Tao Qian
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 31B10: Integral representations, integral operators, integral equations methods
• 45E05: Integral equations with kernels of Cauchy type

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2009
• Tom: 193
• Numer: 2
• Strony: 161-187

Daty

wydano

2009

Twórcy

autor

Andreas Axelsson

• Matematiska Institutionen, Stockholms Universitet, 106 91 Stockholm, Sweden

autor

Kit Ian Kou

• Department of Mathematics, University of Macau, Taipa, Macau, China

autor

Tao Qian

• Department of Mathematics, University of Macau, Taipa, Macau, China

Identyfikatory

DOI

10.4064/sm193-2-4