Hilbert transforms and the Cauchy integral in euclidean space

Tom 193 / 2009

Andreas Axelsson, Kit Ian Kou, Tao Qian Studia Mathematica 193 (2009), 161-187 MSC: 45E05, 31B10. DOI: 10.4064/sm193-2-4

Streszczenie

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.

Autorzy

  • Andreas AxelssonMatematiska Institutionen
    Stockholms Universitet
    106 91 Stockholm, Sweden
    e-mail
  • Kit Ian KouDepartment of Mathematics
    University of Macau
    Taipa, Macau, China
    e-mail
  • Tao QianDepartment of Mathematics
    University of Macau
    Taipa, Macau, China
    e-mail

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