### arXiv:1805.06434 [math.FA]AbstractReferencesReviewsResources

#### Fractional Korn and Hardy-type inequalities for vector fields in half space

Published 2018-05-16Version 1

We prove a fractional Hardy-type inequality for vector fields over the half space based on a modified fractional semi-norm. A priori, the modified semi-norm is not known to be equivalent to the standard fractional semi-norm and in fact gives a smaller norm, in general. As such, the inequality we prove improves the classical fractional Hardy inequality for vector fields. We will use the inequality to establish the equivalence of a space of functions (of interest) defined over the half space with the classical fractional Sobolev spaces, which amounts to proving a fractional version of the classical Korn's inequality.

Sharp weighted Sobolev and Gagliardo-Nirenberg inequalities on half space via mass transport and consequences

arXiv:1710.07953 [math.FA] (Published 2017-10-22)

Characterizations of monotonicity of vector fields on metric measure space

arXiv:math/9603213 [math.FA] (Published 1996-03-24)

Intermediate Optimal Gevrey Exponents Occur