A framework for fractional Hardy inequalities

Abstract

We provide a general framework for fractional Hardy inequalities. Our framework covers, for instance, fractional inequalities related to the Dirichlet forms of some Lévy processes, and weighted fractional inequalities on irregular open sets.

A revised and published version of the paper; 16 pages

References in corpus (1)

• On Harnack inequality and Hölder regularity for isotropic unimodal Lévy processes

Cited by in corpus (10)

• On density of compactly supported smooth functions in fractional Sobolev spaces
• Interpolation theory for Sobolev functions with partially vanishing trace on irregular open sets
• Hardy inequalities and Assouad dimensions
• Hardy and Poincaré inequalities in fractional Orlicz-Sobolev spaces
• The fractional Schrödinger equation with Hardy-type potentials and sign-changing nonlinearities
• The extension problem for fractional Sobolev spaces with a partial vanishing trace condition
• Fractional Sobolev spaces with power weights
• Sharp fractional Hardy inequalities with a remainder for $1<p<2$
• Sharp Hardy inequalities for Sobolev-Bregman forms
• Fractional Hardy-type and trace theorems for nonlocal function spaces with heterogeneous localization