We consider the first-kind Fredholm integral equation , , where A is the Stieltjes transform defined as Under some regularity assumptions on f we prove that the above problem is well-posed according to Tikhonov; that is, for any f in a given class of data there exists a unique solution v of the above equation, and if , , for some positive then , , where is a continuous non-decreasing function with . An expression of the solution v by means of a convergent Fourier series is also given.