Generalized Abel integral operators on spaces with Rooney weights (Q1315056)

The authors study generalized Abel integral equations of the form (with \(0<\alpha<1)\) \[ {a(x)x^{-\alpha} \over \Gamma (\alpha)} \int^ x_ 0{u(t)dt \over (x-t)^{1-\alpha}}+ {b(x)x^{-\alpha} \over\Gamma (\alpha)} \int^ \infty_ x{u(t)dt \over(t-x)^{1-\alpha}} = g(x) \] on the halfline \(x>0\) with respect to Fredholm properties and equivalence to singular integral equations. They work in \(L_ p\)-spaces with weights introduced by Rooney.