First-kind Fredholm integral equations with kernel of Hankel type

We consider the first-kind Fredholm integral equatlon (A upsilon)(x) = f(x), x is an element of R+, where A is the Stieltjes transform defined as [GRAPHICS] 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 upsilon of the above equation, and if \f(x)\ less than or equal to epsilon, For All x is an element of R+, for some positive is an element of then \v(y)\ less than or equal to alpha(epsilon), For All y is an element of [a, b], where alpha(epsilon) is a continuous non-decreasing function with alpha(0) = 0. An expression of the solution upsilon by means of a convergent Fourier series is also given.