Subdomains method for solution of a singular first kind integral equation with Cauchy kernel

The method of subdomains solution of a singular integral equation of the first kind with Cauchy kernel is investigated. A pair of weight spaces, which are the narrowing of the space of continuous functions are introduced. The correctness of the equations on this pair of spaces is proved. Sufficient conditions for the convergence of the method of subdomains in the uniform metric are established.