Affine Poisson & Non-Poisson trace principles for ${\dot{H}}^{-1<-\alpha \le -\frac{1}{2}}({\mathbb{R}}^{n-1})$

This note discovers not only an affine non-sharp-Poisson trace inequality but also its sharp-non-Poisson version for a Sobolev function with the fractional antiderivative.