Fractional Hardy inequality with singularity on submanifold

Abstract

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.

arXiv comment37 pages

References in corpus (4)

• On density of compactly supported smooth functions in fractional Sobolev spaces
• Hardy-Rellich and second order Poincaré identities on the hyperbolic space via Bessel pairs
• Sharp weighted fractional Hardy inequalities
• Boundary Hardy inequality on functions of bounded variation