On a class of two-dimensional singular integral equation not containing complex conjugation of the desired functions

The method of investigating two-dimensional singular integral equations that do not contain complex conjugation of the desired function, used in the study, is externally similar to the method developed by L.G. Mikhailov, which consists of the reduction of this equation to the corresponding homogeneous systems of integral equations with homogeneous kernels of degree -1. Such integral equations occur in many problems in the theory of generalized analytic functions, the theory of quasiconformal mappings and the theory of partial differential equations. In this paper, for one two-dimensional singular integral equations with a discontinuous coefficient not containing complex conjugation of desired functions by passing to an infinite system of integral equations with Cauchy kernel and with homogeneous kernels of degree -1 in the Lebesgue space β-2 2 (𝐷), 1