On certain new Gronwall-Ou-Iang type integral inequalities in two variables and their applications.
We study geodesic completeness for left-invariant Lorentz metrics on solvable Lie groups.
In this paper we give a sufficient condition on the pair of weights for the boundedness of the Weyl fractional integral from into . Under some restrictions on and , this condition is also necessary. Besides, it allows us to show that for any there exist non-trivial weights such that is bounded from into itself, even in the case .