Convergence in the Integral Metric of the General Projective Method for Solving Singular Integral Equations of the First Kind with the Cauchy Kernel

We study a projective method for solving singular integral equations of the first kind with the Cauchy kernel. Depending on the index of the equation, we introduce pairs of weight spaces which represent a restriction of the space of summable functions. We prove the correctness of the stated problem. We obtain sufficient conditions for the convergence of the projective method in the integral metric.