Zeitschrift für Analysis und ihre Anwendungen Vol. 18, No. 2, pp. 379  391 (1999) 

Nonlinear Singular Integral Equations Involving the Hilbert Transform in Clifford AnalysisS. BernsteinS. Bernstein: University of Mining and Technology, Inst. Appl. Math., D09596 FreibergAbstract: We apply operatortheoretical methods for monotone and maximal monotone operators to prove the existence of solutions for nonlinear singular integral and integrodifferential equations involving the Hilbert transform in the Clifford algebra $\Cl_{n,0}$. Properties of the Hilbert transform are proved using Clifford analysis. We generalize wellknown results concerning the complex Hilbert transform and the singular Cauchy integral operator to higher dimensions. Keywords: Clifford analysis, Cauchytype integrals, nonlinear integrodifferential equations Full text of the article:
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