We apply operator-theoretical methods for monotone and maximal monotone operators to prove the existence of solutions for nonlinear singular integral and integro-differential equations involving the Hilbert transform in the Clifford algebra . Properties of the Hilbert transform are proved using Clifford analysis. We generalize well-known results concerning the complex Hilbert transform and the singular Cauchy integral operator to higher dimensions.
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Swanhild Bernstein, Nonlinear Singular Integral Equations Involving the Hilbert Transform in Clifford Analysis. Z. Anal. Anwend. 18 (1999), no. 2, pp. 379–391DOI 10.4171/ZAA/888