Convergence in the integral metrics of the general projective solution method for singular integral equations of the first kind with the Cauchy kernel

We study the projective solution method for 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 the 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 metrics.