Limiting Sobolev and Hardy inequalities on stratified homogeneous groups

TL;DR

This paper establishes conditions under which limiting Sobolev and Hardy inequalities hold on stratified homogeneous groups, extending known Euclidean results to a broader geometric setting, and deriving endpoint Korn inequalities.

Contribution

It provides a sufficient condition for limiting inequalities on stratified groups, generalizing Euclidean cancelling conditions and deriving endpoint Korn inequalities.

Findings

Sufficient condition for limiting Sobolev and Hardy inequalities on stratified groups

Extension of Euclidean cancelling condition to stratified homogeneous groups

Derivation of endpoint Korn--Sobolev and Korn--Hardy inequalities

Abstract

We give a sufficient condition for limiting Sobolev and Hardy inequalities to hold on stratified homogeneous groups. In the Euclidean case, this condition reduces to the known cancelling necessary and sufficient condition. We obtain in particular endpoint Korn--Sobolev and Korn--Hardy inequalities on stratified homogeneous groups.