On Solvability of the Sonin–Abel Equation in the Weighted Lebesgue Space

In this paper we present a method of studying convolution operator under the Sonin conditions imposed on kernel. The particular case kernel is fractional integral Riemman–Liouville operator, other various types kernels are Bessel-type function, functions with power-logarithmic singularities at origin e.t.c. We pay special attention to study close power type functions. main our aim Sonin–Abel equation in weighted Lebesgue space, used allows us formulate criterion existence and uniqueness solution classify solution, due asymptotics Jacobi series coefficients right-hand side.