Multilinear embedding theorem for fractional sparse operators

We show some simple sufficient conditions for which the multilinear embedding theorem holds for fractional sparse operators. By verifying these conditions, we establish the theorem for power weights. We also provide Morrey-type sufficient conditions for which the $L^p \to L^q$, $1<p,q<\infty$, infinitesimal relative bounds hold for Schr\"{o}dinger operators of the form $(-\Delta)^{\alpha/2}+v$.