On Choquet's theory
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 .
We construct a family of continuous functions on the unit interval which have nowhere a unilateral derivative finite or infinite by using De Rham’s functional equations. Then we show that for any