Critical fractional Hardy inequalities

Abstract

We give a roadmap for the study of critical fractional Hardy inequalities for Dirichlet and Sobolev--Bregman forms. We focus on homogeneous forms on the real line, in particular the form of the fractional Laplacian and the Servadei--Valdinoci form. We prove criticality results in both the Dirichlet and Sobolev--Bregman settings.

28 pages, 6 figures