Monotonicity principles for singular integral equationsinCliffordanalysis

In [21] this theorem is used by L. v. Wolfersdorf to consider singular integral equations on the real halfline involving the singular (complex) Hilbert operator. This theory is extended by Askabarov in [1] to the complex case. We want to investigate a special family of singular integral operators in Clifford analysis which has in IR an application to the nonlinear magnetic field equation ([5]) considered by M. Friedman. Electromagnetic processes are described using quaternionic and Clifford analysis by several authors ([2], [3], [4], [6], [7], [8], [10], [11], [12], [17], [18], [19], [22], [23]). These considerations mainly based on the operator D + a. To this subject we want to recommend the book by V.V. Kravchenko and M.V. Shapiro ([13]) and the book by K. Gürlebeck and W. Sprößig ([9]). Singular integral operators are investigated by S.G. Michlin and S. Prößdorf in [16] and especially using Clifford analytical methods by A. McIntosh, C. Li and S. Semmes in [14] and by A. McIntosh, C. Li and T. Qian in [15]. Properties of the Nemickii operator, monoton operators and so one may be found in the book [24] by E. Zeidler.