Higher Order Sobolev-Type Spaces on the Real Line - Bogdan Bojarski; Juha Kinnunen; Thomas Zürcher (Journal of Function Spaces)
This paper gives a characterization of Sobolev functions on the real line by means of pointwise inequalities involving finite differences. This is also shown to apply to more general Orlicz-Sobolev, Lorentz-Sobolev, and Lorentz-Karamata-Sobolev spaces.