Iterated Stieltjes transform of generalized functions

Abstract

The generalized S2-transform of a member of f of a certain space of generalized functions is defined as F(x)=〈f(t),k(x,t;ρ)〉, wherek(x,t;ρ)=∫0∞1(x+y)ρ(y+t)ρ  dy,  ρ>12,0<x<∞  and  0<t<∞. An inversion theorem for the transform is established interpreting the oonvergene in the weak distributional sense.