On the fractional relativistic Schrödinger operator

We collect some interesting results for equations driven by the fractional relativistic Schrodinger operator ( − Δ + m 2 ) s with s ∈ ( 0 , 1 ) and m > 0 . More precisely, for the linear theory, we prove Holder-Schauder-Zygmund regularity results and a Kato's inequality. For the nonlinear theory, we obtain L ∞ -regularity, exponential decay, a Pohozaev-type identity, and a symmetry result for solutions of certain nonlinear fractional problems.