Geometric Hardy Inequalities on Stratified Groups

Abstract

Given a domain in the space, the ‘geometric’ version of Hardy inequalities usually refers to the Hardy type inequalities where the weight is given in terms of the distance to the boundary of the domain. In this chapter we discuss L² and Lᵖ versions of the geometric Hardy inequality on the stratified group 𝔊. For the clarity of the exposition, we first deal with the half-space domains, and then with more general convex domains.