Generalized Stieltjes and other integral operators on Sobolev-Lebesgue spaces

Pedro J. Miana, Jesús Oliva-Maza

For $\mu >\beta >0$, the generalized Stieltjes operators $${\mathcal{S}}_{\beta ,\mu }f(t):=t^{\mu -\beta }{\int }_0^{\infty }\frac{s^{\beta -1}}{(s+t{)}^{\mu }}f(s)ds,t>0,$$ defined on Sobolev spaces $\mathcal{…