Transformation of the Abel integral equation with nonsmooth data into an integral equation of the second kind (Q1974728)

A method of transformation of the linear Abel integral equation with nonsmooth input data into an integral equation of the second kind in the spaces \(L_{p,h}\), \(C^{0+\mu}\) and \(C_{h_2}\) is proposed. The existence, uniqueness, nonexistence and nonuniqueness of its solutions are investigated, and estimates concerning the stability of solutions are obtained. The case when the kernel \(K(\nu,u)\in L_\rho(D_\varepsilon)\) satisfies \[ (\nu-u)^\beta\partial K(\nu,u)/\partial\nu\in L_r (0,\varepsilon, L_\xi(u,\varepsilon)) \] is analyzed.