Displaying similar documents to “Generalized multidimensional Hilbert transforms in Clifford analysis.”

Hilbert transforms and the Cauchy integral in euclidean space

Andreas Axelsson, Kit Ian Kou, Tao Qian (2009)

Studia Mathematica

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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...

Boundedness for a bilinear model sum operator on ℝⁿ

Erin Terwilleger (2007)

Studia Mathematica

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The purpose of this article is to obtain a multidimensional extension of Lacey and Thiele's result on the boundedness of a model sum which plays a crucial role in the boundedness of the bilinear Hilbert transform in one dimension. This proof is a simplification of the original proof of Lacey and Thiele modeled after the presentation of Bilyk and Grafakos.