Published Paper

Inserted: 24 apr 2026
Last Updated: 24 apr 2026

Journal: Communications in Contemporary Mathematics
Year: 2026
Doi: 10.1142/S0219199726500161

Abstract:

We investigate the sharp constant for weighted fractional Hardy inequalities with the singularity on a flat submanifold of codimension $k$, where $1\leq k<d$. 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.