One-sided fractional derivatives, fractional Laplacians, and weighted Sobolev spaces

P. R. Stinga, M. Vaughan

We characterize one-sided weighted Sobolev spaces $W^{1,p}(\mathbb{R},\omega )$, where $\omega$ is a one-sided Sawyer weight, in terms of a.e.~and weighted $L^p$ limits as $\alpha \to 1^{-}$ of Marcha…