Nonlinear singular integral equations involving the Hilbert transform in Clifford analysis.
Bernstein, S. (1999)
Zeitschrift für Analysis und ihre Anwendungen
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Displaying similar documents to “Generalized multidimensional Hilbert transforms in Clifford analysis.”
Nonlinear singular integral equations involving the Hilbert transform in Clifford analysis.
Linear and bilinear Hilbert transform.
Bučkovska, Aneta (2001)
Novi Sad Journal of Mathematics
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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...
The Hilbert transform and rearrangement of functions
R. O'Neil, G. Weiss (1963)
Studia Mathematica
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Generalized Moisil-Théodoresco systems and Cauchy integral decompositions.
Blaya, Ricardo Abreu, Bory Reyes, Juan, Delanghe, Richard, Sommen, Frank (2008)
International Journal of Mathematics and Mathematical Sciences
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On the bilinear Hilbert transform.
Lacey, Michael T. (1998)
Documenta Mathematica
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Hermitean Cauchy integral decomposition of continuous functions on hypersurfaces.
Blaya, Ricardo Abreu, Reyes, Juan Bory, Brackx, Fred, De Knock, Bram, De Schepper, Hennie, Peña, Dixan Peña, Sommen, Frank (2008)
Boundary Value Problems [electronic only]
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Hermitean Téodorescu transform decomposition of continuous matrix functions on fractal hypersurfaces.
Abreu-Blaya, Ricardo, Bory-Reyes, Juan, Brackx, Fred, De Schepper, Hennie (2010)
Boundary Value Problems [electronic only]
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The Heisenberg group and the group Fourier transform of regular homogeneous distributions
Susan Slome (2000)
Studia Mathematica
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Hilbert transform and its geophysical applications
V. Červený, J. Zahradník (1975)
Acta Universitatis Carolinae. Mathematica et Physica
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Hilbert transformation of Beurling ultradistributions
S. Pilipović (1987)
Rendiconti del Seminario Matematico della Università di Padova
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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.