Weighted fractional Hardy–Sobolev and Hardy–Sobolev–Maz’ya inequalities with singularities on flat submanifold

We investigate the sharp constant for weighted fractional Hardy inequalities with the singularity on a flat submanifold of codimension [Formula: see text], where [Formula: see text]. We also prove a weighted fractional Hardy inequality with a remainder. Using this result, we extend and derive a weighted version of the fractional Hardy–Sobolev–Maz’ya inequality with singularities on a flat submanifold. Furthermore, we obtain a weighted logarithmic fractional Hardy–Sobolev–Maz’ya inequality in the case of a singularity at the origin and we show that in this case, the fractional Hardy–Sobolev–Maz’ya inequality does not hold.