On Weighted Fractional Integral Inequalities

The paper is devoted to integral inequalities for fractional derivatives within the weighted L2 setting. We obtain a necessary and sufficient condition for the operator (−Δ)λ in Rn, 0<λ<n/2, to possess the weighted positivity property where the weight is the fundamental solution of the operator. The best constants in a two parameter family of Hardy–Rellich type inequalities are found. Some other related inequalities are studied.