Fractional Hardy inequality with singularity on submanifold

We establish fractional Hardy inequality on bounded domains in ${\mathbb{R}}^d$ with inverse of distance function from smooth boundary of codimension $k$, where $k=2,\dots ,d$, as weight function. The case $sp=k$ is the critical case, where optimal logarithmic corrections are required. All the other cases of $sp<k$ and $sp>k$ are also addressed.