On Smoothness of the Abel Equation Solution in Terms of the Jacoby Series Coefficients

In this paper we continue the investigation of the Abel equation with the right part belonging to a Lebesgue weighted space. We have improved the previously known result - the uniqueness and existence theorem formulated in terms of the Jacoby series coefficients that gives us an opportunity to find and classify a solution due to an asymptotic of some relation containing the Jacoby coefficients of the right part. The new main results are in the following: The conditions imposed on the parameters, under which the Abel equation has a unique solution represented by the series, are formulated; The relationship between the values of the parameters and the solution smoothness is established. The independence between one of the parameters and the smoothness of the solution is proved.